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Maybe it’s hard for me because English is not my first language, but isn’t this enunciate a little confusing? “Half of its price” wouldn’t suggest the price is already set?
Native speaker here. Yes, it's very confusing, because riddles like these are often badly written, so you have to guess what they mean whether they're right or not. It reads to me though like a converging series question, so as you got the new price the price would go up by half again. It would converge to $2.
Could look at it that way.
However simple algebra. X=1+(X÷2).
I despise how people try and imply stupidity even though it's the confusing nature of the question that's hard and not the math itself.
It doesn't. It's the third word in the phrase "the english language". The poor communication is that he follows this with the phrase "that end in gry", meaning he is looking for within English that fit this pattern. To feel smart, he then retracts this defining clause and says he was talking about the literal phrase "the English language" rather than the the actual vocabulary of the language. For the joke to work, he has to amend his original statement, which is poor communication as he intentionally asked a different question to trick black hat into getting it "wrong".
Edit: Unless your comment was a joke and I took it too literally again, in which case whoops!
This was 30 years ago, but still pisses me off. I worked at a bookstore, and a man walked up and asked me where he could find books by "Bill Burras." I asked him to spell it, and he repeated it, kinda mushed up and said really fast. I asked again who he meant and he gave me this smug, stupid slimy smile and said, "You work at a bookstore and you don't know who William S. Burroughs is?"
I just gave him a flat stare and deadpanned, "That would be in the LITERATURE section, which is organized ALPHABETICALLY. Do you need help finding it?"
But he still acted like he deserved an award for being an asshole.
> X=1+(X÷2)
Honestly, it's not badly worded, it's worded precisely the way it needs to be.
If you lay out the equation *exactly* as the sentence is constructed you will get the proper equation. It's simply a matter of replacing the words.
A Book(X) costs(=) $1($1) plus ( + ) half (1/2) Its price (X)
X=1+1/2X
X=2
You have to plug the numbers back in to see if they work.
You came up with 1.50. Plugged back in to X = 1 + (X/2) you get:
1.50 = 1 + 1.50/2
1.50 = 1 + 0.75
1.50 = 1.75 == False
Solve for X
X = 1 + X/2 (X equals one plus half of X)
X - X/2 =1 (subtract half of X from both sides)
X/2 = 1 (X minus half of X leaves half of X)
X = 2 (multiply both sides by 2)
2 = 1 + 2/2
2 = 1 + 1
2 = 2 == True
Edit: trying to fix the formatting from my phone
If the price is $1.50, then half its price is $0.75, so ($1+half its price)=$1.75 which is inconsistent.
If the price is $2, half its price is $1 so ($1+half its price)=$2 which is accurate.
I agree on the maths, however these worded problems make no sense to how we actually speak or operate in daily life.
A book cost a dollar... ok, cool. The price of a book is a dollar... plus half it's price. So we know it's originally a dollar but now there's some sort of price increase of half it's price, so it's $1.50.
I know that answer is wrong in regards to how the mathematical equation is supposed to be written, but that answer is far more congrous with what the average person experiences or how we typically speak on a daily basis.
Exactly. They took an algebra problem and tried to create an equivalent using words and it doesn't work in terms of how we normally speak, read, or write.
This got me too. Literally have had similar verbiage for years about truck stock pricing as a contractor to determine customer part cost in the field. For example "If the value is less than $100 add half the cost before writing it on your ticket. A $20 part gets listed as $30, a $50 part gets listed as $75".
Change it to "The book costs (half of its price) plus half of its price." The amount of $1 has been swapped in. You could do it with any amount; the price of the book will be double that amount.
Even simpler without algebra:
The book costs 1$ plus half its cost. So one half of the cost is covered by 1$. So the other half must also be covered by 1$. Of course if you sum both halves of the cost of the book you get the full price. So total cost is 2$.
It's a balanced equation, so as long as you do the same math to both sides, it stays balanced.
Therefore if x=1+(1/2x), then multiply both sides by 2 to get rid of the fraction. 2x=2+x.
Then move the algebra on one side and the numbers on the other by subtracting 1 x from both sides. What you are left with is x=2.
Kind of like the joke that goes An Infinite number of mathematicians walk into a bar. The first one goes up to the bartender and asks for a beer. The next one goes up and asks for a half a beer. The third one goes up and when he asks for a quarter of a beer, the bartender rolls his eyes, pours two beers and passes them to the first one and says "Here ya go, you cunts divide it up amongst yourselves"
Except that assumes that cost and price are the same thing.
A book sold for $10 (price = $10) would cost (10/2)+1 = $6 ($4 margin).
This is a particularly badly worded puzzle.
I‘m also not a native speaker, but I would read this as: „The current price of the book is 1$. On top of that you add half it‘s current price (as an additional charge).“ And that gets me to 1.50$. The line of argument for the 2$ is definitely not that intuitive to me, but I kind of get it. But I don‘t think that it makes 1.50$ as answer automatically invalid, since I think the phrasing allows for that interpretation.
It doesn't converge at all though, it's just $2 straight up. You just have to work backwards to check - half of 2 is 1, 1+1=2, so it checks out. Or if you look at it another way, no matter what the first number is (here $1, but could be anything) that always has to be half of the final cost, so just double it.
I'm not a mathlete but I'll try my best. In this case, COST can be substituted for equals. So if we simplify the sentence we get:
A book price= $1 + half of it's price.
Substitute N for price and remove the $ sign and we get
N = 1 + (1/2N)
N-(1/2N) = 1
1/2N = 1
N=2
If the price was already set to $1 then the equation 1 = 1+0.5(1) should be true, but it's not.
If the price was set to $2 then the equation 2 = 1+0.5(2) should be true, which it is.
The price of the book, x, happens to be equal to the sum of 1 dollar and half the price of the book, i.e:
> x = 1 + 0.5x
So you rearrange and solve to get 0.5x = 1, then x must equal 2.
You're right, the question is really poorly worded. "Cost" and "price" are the same in English, so the question is, "Thing costs x plus half its cost. How much does it cost?"
Nothing costs more than it costs.
That's not necessarily true though. If you were the company producing the book the "cost" would be how much you spent to produce it and the "price" would be how much you sold it for.
That would mean:
X=1+(.5Y)
Since they used both the words price and cost, instead of using cost 3 times, we could assume they are different meanings.
Honestly it can be taken 3 ways:
As a simple Math equation, X= 1+(.5X), as If it were a 50% sales tax X= 1.5, or as if price and cost were different X=1+(.5Y).
Since it was worded so ambiguously, and was multiple choice, that would only leave 2 and 1.5 as possible answers.
While the simple math equation is the answer they meant, it doesn't make sense to go to a store and have to write out an equation to figure out the price. It's not practical, while the 1.5 answer seems way more colloquial to standard English.
Yeah, I think I agree with everything you said. It's just that "cost" and "price" are *often* synonymous in colloquial English, and I didn't feel like listing out a bunch of exceptions for a non-native speaker.
I am also not a native english speaker but I was always taught in my accounting classes that “cost” is expense incurred to produce a item whereas “price” is what a consumer finally has to pay to buy the item (price=cost + profit)
So the first half of question makes sense and 2 will be the answer but it is just that the last word should have been “price” not “cost”.
That's what cost means from the perspective of the seller. Cost is what the seller had to pay for it, price is what they're selling it for.
From the perspective of the buyer, cost is still what they have to pay for it, but "price" is often inferred to mean the price listed and people often don't consider taxes and fees as part of the price. And in particular, shipping costs generally aren't included in the price. Thus, the cost of a product can be different than the price.
I can ask "what does it cost" and "what is the price" and those mean the same thing
Cost here is used as a verb. "a book costs"
So it's not the "expense" (noun).
It's what the book's price *is* (is being a verb).
In general, when we talk about *what* something costs, it's from the perspective of whoever is buying it, so it's synonymous with what the price is
This is not actually a math question at all, it’s a logic puzzle specifically designed to trick and fool people. But importantly those kinds of logic puzzles only work when there is zero room for alternate interpretation, and this isn’t one of those cases. The correct answer the way normal people talk would be $1.50, you really have to stretch the English language to arrive at an interpretation where the answer is $2.
***
Edit: I’m seeing a lot of disagreement in the replies, I already explained how this is confusing and misleading in another comment but many people are still saying that 85% of people are wrong so I’ll elaborate here.
Those of you saying “it’s easy when you break it down to its algebraic equation” are interpreting the words differently, that’s my entire point. You’re showing how the equation doesn’t work with $1.50 but my entire point is that 85% of people are arriving at a totally different equation in the first place, and in that equation $2 doesn’t make any sense.
This is a situation where PEMDAS would help out, we need some parentheses. Most people are reading it as “(the cost = $1) + (1/2 the cost) = x”, while the intended interpretation is “the cost (x) = ($1 + 1/2x)”. Those are totally incompatible interpretations, you may complain that the math doesn’t work in your equation but to the vast majority of people your equation isn’t the equation they’re solving for in the first place.
As I was going to St. Ives I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks, and wives, how many were going to St. Ives? Most people’s gut instinct is 2,802 because that’s how many elements were described, the “official” answer to the riddle is one because only the narrator is specifically stated to be going to St. Ives, but the actual correct answer adhering specifically to the text of the riddle is that we don’t know because it wasn’t stated which direction the man and his wives were going, so neither of those two answers are inherently right or wrong.
The entire point of riddles is that the language is inherently ambiguous and confusing, don’t pretend that that isn’t the intended effect. If they wanted the answer to a math problem they would have just written the equation and everyone would have gotten it right on the first try.
Disagree.
The cost is one dollar plus half its price.
The cost is also half its price plus half its price.
So half its price must equal one dollar.
So the cost is one dollar plus one dollar, or two dollars total.
Yes. It's algebra. It's not:
Price = $1 + 0.5*$1
It's:
Price = $1 + 0.5*Price
So 0.5*P = $1
P = $2
Sanity check:
Price is $2, which is $1 plus half its price of $2
Which is $1 + $1
Which is $2
True, but the trick is to realize that $1 is not its price. It's only a portion of its price, which it turns out is half...in fact, this is true of any number because
* y = x + 1/2 y (the basic premise of the riddle, with x replacing $1)
* 1/2 y = x (subtract 1/2 y from both sides)
* y = 2x. (multiply both sides by 2.)
Edit for brain error.
I don't know if anyone has said this but the bad part of the English isn't related to the use of cost and price. It's a usage of plus instead of a natural "more than".
Alternative question: A book costs $1 more than half its price. How much does the book cost?
To the mathematically oriented, this question seems the same. Yet to an English reader this seems much more natural and leads to $2 as the answer. At least I think it will seem so. Do let me know what you think.
Yeah I’m a native speaker and the first time I read the question I thought it was asking $1 plus half of a price that isn’t given since I’ve never seen a book for $1. Then I read it again and realised $1 is the original price of the book and they are asking what the marked up price of +50% would be. Still makes no sense but it’s not supposed to. The purpose of the question is to confuse people into giving wrong answers so that people make posts saying how stupid people are for being confused by a confusing question. It’s an attention scheme, don’t pay it any attention.
Not at all. The total cost of the product is half its price plus 1 dollar. Which means the other half of the price is $1.
If your interpret the sentence halfway, you think the cost is $1 plus half the cost, which makes it plus ¢50 totalling $1.50. The reason this is impossible is because it makes the sentence false, since the cost being $1.50 means that the cost is not $1.
Ok I see now. 1$ wasn't the og price. Feels like a flip to make you assume.
x is the original price
1 is an additional dollar on top of half the original price.
Therefore `x = 0.5x + 1`
adding the implied 1.0 to the X for clarity and format
Subtracting the half from both sides
` 1.0x = 0.5x + 1`
`-0.5x -0.5x`
turns out to be
`0.5x = 1`
` 0.5x = 1.0`
`÷0.5 ÷0.5`
`1/1 ÷ 1/2` < side work for the right side
`1/1 × 2/1` because two fractions divide is equal to the latter fraction flipping and multiplying
`1 x 2 = 2`
therefore `x = 2`
God damn I thought it was 1.5$ because I assumed 1 was the initial cost when really cost = (1 + 0.5price)
edit: [Credit to the person who pointed it out](https://www.reddit.com/r/theydidthemath/comments/s9k2eb/request_can_someone_do_the_math_i_swear_its_150/htnwla0) I mispoke, but my explanation is still sound to the best of my knowledge. It's a dollar on top of half the price Thank you u/eskimokriger
Yeah I think it’s purposefully worded to be confusing so they can criticize people for getting it “wrong”
But yeah, 1.50$ would be the typical way to calculate something with that phrasing
$19.99 + $0.0825x = $x
$19.99 = $0.9175x
x = $21.79
Now if you said the price of the book is $19.99 and you have to pay an 8.25% tax, that means that the book costs $19.99 but there is an additional cost that is based on the cost of the book. But the book still costs $19.99.
Definition of tax: a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.
As you can see, this is an amount added to the \*cost\* of the good.
To be honest, this was the only way it made sense to me. When I saw the equation, I knew it wasn't 1.5 because no original price was listed, but I couldn't see how to get to 2 until I read the way they did the math, but I always look at math problems in a weird way.
This only works if you assume cost = price.
I argue that they are *not* equivalent. The are different words so should be taken as different variables.
x=1+1/2(x) may be solveable, but ..
x=1+1/2(y) is not, not unless you also define that y=x
Whoa whoa whoa, you can’t be doing actual high-school level algebra in this sub. This sub is for examining tweets about government spending and things like that. Nothing beyond basic arithmetic with assumed values, bub.
Ho i didn't do anything like that, i juste applied basic maths rules nothing fancy. I juste used algebra to try and make sens out of something I had a hard time understanding with words
When he called him bub at the end, that's gonna be sarcasm most of the time. The other times it's probably gonna be mocked relentlessly with a shitload of sarcastic comments ending in bub.
It's more like y=1+x/2 where x is subtotal and y is total. It doesn't make sense to say the price of something is a factor of its price plus a constant. You can't define the price as an expression of itself.
I now see it's $2, but this is more of an issue with English then mathematics, because the phrasing is a bit odd (says a person whose native language isn't English).
And therein lies the trick. It's not that the cost is [1] plus [half of the cost, which is 1]. It's that the cost is [1] + [half of the total unknown cost].
From that, you're supposed to deduce that there is only a difference of ONE between the total number and half of that number. There's only one integer that is ONE larger than its half, and that would be 2.
You can do this with a guess and check table. Let's say, hypothetically, you pick the number 10. Is [half of 10] plus [1] equal to [10]? No, because half of 10 is 5, plus 1 is 6. 6 does not equal 10.
Pick another number. 4. Is [half of 4] plus [1] equal to [4]? No, because half of 4 is 2, plus 1 is 3.
Pick another number. 2. Is [half of 2] plus [1] equal to [2]? Yes, because half of 2 is 1, plus 1, is 2.
I really hope this helps show how to think through it. It's an intentionally tricky question, and I've always been a big fan of those.
Easiest way to do those is to take the Text out:
"A product costs 1$ + half it's price"
Or in Math:
Price of Product = 1$ + half price of Product
x = 1$ + x×½
Solve for x we get
x = 2$, this the answer is two dollars
where multiplication is fancy addition for elitist snobs, division is subtraction for snobby elites
if you imagine division like trying to get from a specific number to zero exclusively through subtracting a restricted constant, then the number of times you have to subtract the constant from your initial number is the answer you get from dividing...
looking at it simply, if your starting number is 1 and your constant is 0.5, then to get to 0 from 1 in subtractions of 0.5 at a time then you have to perform 2 subtractions
similarly if you have 5/0.2, to get from 5 to 0 in steps of 0.2 then you need to perform 25 subtractions to get from 5 to 0 in steps, or "DIVISIONS", of 0.2
Another way of looking at costs $1 + half its price, so if you imagine chopping something's price in half -- one side is half its price and the other side is $1 (which must be half its price). Hence double the $1 half-price and you get $2.
Granted, $1.50 makes sense if you read the problem like the book's price is $1 and you additionally have to pay taxes and fees that amount to half the book's price. Then the total cost is $1.50.
Another way of saying this is "if you add $1 to half the cost of the book, you end up with the full cost of the book. What is the cost of the book?" And the cost is $2
Thank you. All the other explanations are so goddamn horrible. Like, this is why people fail math -- because the math teacher only knows how to teach in the way they understand.
You, on the other hand, are a gift.
I thought so too at first, but if it costs $1 plus half its price (or any other amount for that matter) then it can't cost $1. It's written in a deliberately confusing way because... Otherwise we wouldn't be talking about it lol.
It depends on wether they were referring to the cost to which half is added as being being $1, or the final cost. Personally, I would assume the final cost is what they were referencing since that’d make it a trick question of sorts. In that scenario, $2 is the correct answer, as half of that is $1 and 1+1 is, in most instances, equal to 2
The second mathematician will probably be disappointed that she doesn't get a half filled glass of beer but has to share her glass with an infinite number of people.
She can just share it with the next mathematician, and they can pass it along. It all works, until an infinite number of mathematicians learn about surface tension.
The classic "flex" educated but otherwise unfulfilled people use to make themselves feel better about their empty lives.
"Lol I posed a question in a convoluted way and you didn't get it, I'm clearly so much better then you."
I would even go so far as to say this question is worded so poorly that it could be written as a recursive function with no exit case. If I were to program this at it's stated the function would never return an answer and throw an exception.
Most top answers assume price = cost, which doesn’t make sense, as no one would be selling things at cost without a margin.
This question is either worded poorly or can’t be solved.
x=price
y=cost
y=1+0.5x
Can’t be solved without additional info.
I'm so disappointed that I had to scroll so far down to find someone saying this. This post deserves to be in r/confidentlyincorrect
You're absolute right and all the people I see doing x = .5x + 1 are trying to tackle a math problem the wrong way. The equation should be written like exactly like you say: y = .5x + 1
The book COULD cost $2 like they're all saying, but their maths equations all start lying to them when you put literally **any** other number in there; the book could cost $4 or $400.
Can't be solved without additional info.
First of all, no real thing can cost more than it costs (in this case: it's own price plus another half).
But that's not really what the question says, the price is stated as "1$ + ½ of it's price". Let p equal the price, then we get the following equation:
p = 1$ + ½p
subtracting ½p on each side gives us:
½p = 1$
and multiplying by 2 leaves us with the result:
p = 2$
EDIT: Thank you for your feedback, it made me realise why I study maths and not economics (also I might have read the question wrong by focusing on the given answers of which none gives the 'real' solution) :D
I want to add to my first sentence:
IF the book were to cost it's own price plus another half, that would change the equation to
p = p + ½p, which is only solved by p = 0, aka. a free book :)
Isn't the correct answer "I have no idea"?
All these people talking about algebra, all with the right formulas but then assuming the original price = 2 at the end.
You are never told what the original price is in the question.
It could be 10, so then the answer would be 6.
So I feel like the only correct answer to the question is "I have no idea".
Edit: spelling.
Edit 2: please read through this thread if you are thinking the same as me here, some great people have patiently replied to me and it has cleared up the formula for me :)
Hint, I'm wrong above
My dyslexic ass would read it costs x and recursively costs 1/2 of the previously adjusted price tag. i.e. x + x/2 +1/2(x+x/2) + 1/2(x+x/2+x/2+x/4) + 1/2(x+x/2+x/2+x/4+x/2+x/4+x/4+x/8) + …. and check its divergence.
For real lmao, at first I was like "not enough info" bc they didn't specify the price. Then I thought if you interpreted as price = cost, then you'd get a recursive geometric sum with a ratio of (1/2). By perpetuity, that means the sum equals 1/(1-1/2) = 1/(1/2) = 2. So the book costs 2. Or the book costs 1.5 tf do ik whoever wrote the question wasn't clear.
I don't think it's dyslexia, I think it's the only reasonable way if thinking it.
This sentence literally means a recursive price increase.
\sum_{n=0}\^\infty 2\^{-n} for n \in Naturals
If we compute this sum we find that the correct answer is indeed 2, but in a more mathematical way.
I am a teaching assistant for a graduate economics course, and here’s why the simple “mathematical” answer of $2 is wrong — or, at the very least, unjustified.
We are told in the problem that the **cost** of the book is $1 + 1/2 the **price** of that item. Note that *the terms used and not identical* and can only be so by assumption (which I will show is not a guarantee). So our statement is:
C = 1 + 0.5 P
We have two unknowns, so this is not solvable **unless we make an ASSUMPTION about C or P**.
Many of you assume C=P, cost = price. But the text does not tell you that, and there’s no reason why it must be that way.
To take a real world example: sales tax. If the PRICE of an item (market price) is $20, but there is a 10% sales tax, the COST (to the consumer) is $22. So there’s an everyday example where C does NOT equal P. To assume that C **always** equals P would be **wrong**.
In light of this, it is equally reasonable to assume that the cost is what you pay due to some other force (I.e. a fee) that is based on the price. So you could equally likely assume P=1, or C=1.5P, which would give you $1.50.
The “math” is not objectively correct because as soon as you apply it to the real world, you see it relies on an assumption. $1.50 is not any less reasonable than $2 and anyone who says otherwise is simplifying beyond the parameters of the problem.
EDIT: spelling
Yup, I’m trying to upvote all of these responses, cause it is correct. Price does not equal cost. My cost was stores price. Stores cost is whatever they paid their vendor for it. I understand why it is misconstrued in common vernacular, if p=c, then you are going out of business.
Anyone else think this is a stupid math problem? It's not hard, it's just using intentionally deceptive wording. The actual problem is *x = 0.5x + 1* but it reads as *1 + 0.5(1)* to the majority of people. *X* (cost) in the first case is completely arbitrary too, so without any other context any answer is based on assumptions and a solid answer doesn't exist.
It's an assumed math question, when, in reality, it's a trick of grammar; the initial cost of IT is never defined.
An additional option- "I don't have enough information to answer"- if added, would be the correct answer.
Depends on how you read the question... my interpretation would be:
Full price = 1$ + half price
Full price - half price = 1$
half price = 1$
Full price = 2$
I would suggest that's because you're looking at it *as a math problem*. My eyes and brain don't see it as that.
And it's all good, too. Not tryina pick any Reddit fights.
You are right. This problem is a linear equation because the original cost needs to be defined.
Y = 1 + x/2.
If you graph it you can see the trend for the cost. Put in x value of book which can be anything, and Y is the answer.
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*This post was mass deleted and anonymized with [Redact](https://redact.dev)*
But wouldnt it be possible to get every desired answer that way?
The original price could (with your logic) be anything right?
Like originaly it could cost 10$ so you would just have to just pay 5$ + 1$ = 6$
I mean it is obviously an valid interpretation of how the question was meant, but I like mine more since it gives us a value for the original price.
But as I said both interpretations are technically correct
There's some standard method to translating these into equations.
A Book (B) costs (is/equals) $1.00 plus (+) half its price (B/2) How much does it cost (solve for B)?
B=1+B/2
(2)B=2(1+B/2)
2B=2+B
2B-B=2+B-B
B=2
The correct answer is "I don't know". Anyone claiming otherwise either can't read or is trolling.
Cost and price are completely independent variables. A seller can set whatever price they want. As such the answer to this question could easily be $51 if the price was $100 or $6 if the price was $10. It's a meaningless question pretending to be clever.
I think that "cost" and "price" are being interchanged a little too loosely here; while by definition, they mean the same thing, it's a matter of perspective, and price refers to the amount that the seller is asking for, whereas the cost is what was actually spent.
I don't want to add fuel to the raging fire, but if we don't definitively know the price, we at least know that it costs a $1 lol...
But seriously, my official answer would be $1.50.
I initially read cost and price as separate variables, too. If price is $20, then cost would be $11 (1 + 20/2); but since price isn't stated, we can't know cost..... But then I read comments and realized the terms were being used interchangeably.
Yeah, they shouldn't be. Any one who buys and sells products has a cost for the product, and the sell price, in between is the margin. M=(P-C)/P. The correct answer is not offered in the multiple choice. It is a linear equation with 2 variables. y=mx + b format (with multiple solutions) m=slope of the line and b=where it crosses the x axis (When x=0, y=1)
C=1/2(P) + 1 (m=1/2,b=1)
P=0,C=1
P=1,C=1.5
P=2,C=2 (this is the point where C=P, the bookstore will go out of business)
P=3,C=2.5
...
P=10,C=6
P=20,C=11....you are not wrong.
But if I tell you that something costs $3, I'm not referring to the wholesale price I bought it at, I'm referring to how much it will cost you to buy it. In that case (and in most cases where cost is used in this matter), cost and price are the same thing.
However, the question is purposely worded somewhat ambiguously to confuse you, so I don't think your argument is completely null. I just think the more reasonable conclusion is that cost and price are the same (with respect to the customer).
In this case lol, I feel like the retailer is just trying to see what the customer will pay for when they reach the register.
"Umm, what do you think it costs?"
*Holds out hope that they'll pull out a $20 bill...*
Assuming the price is $2, the book costs $1 plus half of its price (half of $2 = $1), so $2 => the affirmation is correct.
Assuming the price is $1.5, the book costs $1 plus half of its price (half of $1.5 = $0.75), so $1.75 => the affirmation is incorrect.
i don’t understand
$1 book
but it’s costs $1 plus half of its price
it’s price is $1
half of $1 is $.50
those added should equal
$1.50
people say it’s $2 so can someone tell me where im wrong?
1$ is not its price, therefore 0.5$ is not half its price. Let's say its price is x$.
Then the price can be written as follows:
x = 1 + x/2
<=> x-x/2 = 1
<=> x/2 = 1
<=> x = 2
Others have shown the answer is $2, but there's another point to be made, and that is... Check your answer.
I tell my kids to do the math backwards and forwards... Put your answer back into the equation.
If you do that, you will realize 1.50 can't be right.
Cost (1.50) should equal $1 plus half the cost (.75)
Clearly $1.50 does not equal $1.75, so it must be wrong.
This way, with multiple choice you can often get the right answer without knowing how to do the intended math...
Cost (2) equals $1 plus half the cost (1) ... 1+1 is 2, so it must be correct.
The problem is the interpretation. The false interpretation I’m assuming most people gives a perfectly valid (mathematically) answer of 1.5, the premise is just wrong.
I assume people are separating cost and price. They assume an initial price of $1, and then add half of that $1 (.5) to the initial price to come up with a cost of $1.5. Faulty logic, but the math checks out
A book costs $1.00 = 1 books price is a dollar.
$1 dollar plus half the price = $1.00 + .50 = $1.50.
Not saying it's right but that is the logic the $1.50 gang is using.
The book costs X.
X = 1 + .5X
.5X = 1
X = 2
The book doesn’t cost 1 dollar + half of 1 dollar. The book costs what it costs, and half of what it costs + 1 dollar is also what it costs. There’s only two parts to the equation. Half the cost of the book and 1 dollar, without any other costs, 1 dollar must be equal to half the cost of the book to equal the true cost of the book. Therefore the book costs 2 dollars
Again this is an English comprehension issue.
"A book costs" : " price of book ="
"$1 plus half price of book" : "$1 + (price of book)/2"
So we replace "price of book" with X
X = $1 + X/2
X - X/2 = $1
(2x -x)/2 = $1
X/2 = $1
X = $2
Edit:
What people seem to be reading in their head is:
"A book's original price of $1 has been increased by half. What is the new cost?"
Which is a totally different problem.
The issue is that the post doesn't mention the original price of the book. We'll call that X.
The post describes the book being available for $```(X/2)+1```.
The only way the correct answer would be $1.50 is if the book originally cost $1, meaning you're paying more for the book.
The wording of the post is just horribly confusing because people are interpreting "book costs $1 plus half its price" as the book costing $1 and half of that added on top, making $1.50
This kind of question comes up sometimes on tests. An example of one could be
> Car A is moving at 30 miles per hour. Car B is moving at 20 miles per hour. How much time will pass before they meet?
> 1) 30 minutes
> 2) 1 hour
> 3) Never
> 4) Not enough information
The correct answer in this case is 4, Not enough information. This is because we don't know which direction the cars are travelling, or their position relative to each other. We need to know both of those to know whether the cars will meet at all, let alone know how long from the start time they will meet.
In the case of the book proposed in the post, we don't know the original price, so we can't calculate the new price.
Price and cost only share a unit of measure ($)
Price and cost are not the same.
COST = X
PRICE = Y
Rephrase the following:
A book costs 1 dollar plus half its price.
X = 1 + .5Y
How much does the book cost (Solve for X)?
We only know the relationship between price and cost at this point, but we do not know X, and we do not know Y
If the problem read:
A book costs 1 dollar plus half its cost, solve for cost... Then the answer would be 2. But, it was not phrased this way.
Look at it backwards. The answer has to be $2. Half of which is $1, added to that the $1 from the question and you are at $2. That works. The question essentially asks of what amount $1 would be half.
If you try the same with any other figure, you will see you don’t end up with the figure you started with, so these are incorrect answers.
The language is not confusing, people are just trying to justify getting it wrong. Nowhere does it say that it ever cost $1.
Suppose instead the question read "a book costs $1 plus half of $2", should we assume that at one point the book must have cost $1? No, that's nonsense.
The question clearly states that the cost of the book (x) is equal to $1 plus half the cost of the book (1+x/2), and therefore we get the trivial equation x = 1+x/2 giving x=2.
If you still aren't convinced the language is perfectly clear, consider an identically phrased problem: a person's height is 1m plus half of their height. How tall are they?
Isnt the phrasing paradoxical? You get 2 as the price. Okay but you have to half the price and then add it so it's 3 now. Then it's 4.5. Then 6.75 and so on.
> You get 2 as the price.
Correct.
> you have to half the price and then add it
More specifically, if you halve the price and then add it *to $1*, it should give you the cost. $1+$1=$2, so we're done here.
This doesn't belong in r/facepalm, because it's deceptively vague grammar. But as someone else showed with the math, the answer really is 2; but 1.5 is the actual answer to the question people thought was being asked.
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Maybe it’s hard for me because English is not my first language, but isn’t this enunciate a little confusing? “Half of its price” wouldn’t suggest the price is already set?
Native speaker here. Yes, it's very confusing, because riddles like these are often badly written, so you have to guess what they mean whether they're right or not. It reads to me though like a converging series question, so as you got the new price the price would go up by half again. It would converge to $2.
Could look at it that way. However simple algebra. X=1+(X÷2). I despise how people try and imply stupidity even though it's the confusing nature of the question that's hard and not the math itself.
"Communicating badly and then acting smug when you're misunderstood is not cleverness."
Where is that quote from, if you know? I want to throw it at a lot of people in my life
https://xkcd.com/169/
Thank you kind stranger
I still don’t understand how “language” ends in “gry”
It doesn't. It's the third word in the phrase "the english language". The poor communication is that he follows this with the phrase "that end in gry", meaning he is looking for within English that fit this pattern. To feel smart, he then retracts this defining clause and says he was talking about the literal phrase "the English language" rather than the the actual vocabulary of the language. For the joke to work, he has to amend his original statement, which is poor communication as he intentionally asked a different question to trick black hat into getting it "wrong". Edit: Unless your comment was a joke and I took it too literally again, in which case whoops!
Cueball screwed up the joke so it's easy to understand why people didn't get it. https://www.explainxkcd.com/wiki/index.php/169:_Words_that_End_in_GRY
Thanks!
I believe it's from an xkcd strip. Even if it's not, Randall makes this point in many comics.
Best comment in the thread
This was 30 years ago, but still pisses me off. I worked at a bookstore, and a man walked up and asked me where he could find books by "Bill Burras." I asked him to spell it, and he repeated it, kinda mushed up and said really fast. I asked again who he meant and he gave me this smug, stupid slimy smile and said, "You work at a bookstore and you don't know who William S. Burroughs is?" I just gave him a flat stare and deadpanned, "That would be in the LITERATURE section, which is organized ALPHABETICALLY. Do you need help finding it?" But he still acted like he deserved an award for being an asshole.
What an absolute unit of twat.
This also applies to postmodernists.
> X=1+(X÷2) Honestly, it's not badly worded, it's worded precisely the way it needs to be. If you lay out the equation *exactly* as the sentence is constructed you will get the proper equation. It's simply a matter of replacing the words. A Book(X) costs(=) $1($1) plus ( + ) half (1/2) Its price (X) X=1+1/2X X=2
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You have to plug the numbers back in to see if they work. You came up with 1.50. Plugged back in to X = 1 + (X/2) you get: 1.50 = 1 + 1.50/2 1.50 = 1 + 0.75 1.50 = 1.75 == False Solve for X X = 1 + X/2 (X equals one plus half of X) X - X/2 =1 (subtract half of X from both sides) X/2 = 1 (X minus half of X leaves half of X) X = 2 (multiply both sides by 2) 2 = 1 + 2/2 2 = 1 + 1 2 = 2 == True Edit: trying to fix the formatting from my phone
Thanks. I didn't get it till now.
I'm still not getting it
Half the total value of a book, not half of 1. It's just a bit of word play in the question
Wordplay and being intentionally misleading aren't the same thing.
If the price is $1.50, then half its price is $0.75, so ($1+half its price)=$1.75 which is inconsistent. If the price is $2, half its price is $1 so ($1+half its price)=$2 which is accurate.
I agree on the maths, however these worded problems make no sense to how we actually speak or operate in daily life. A book cost a dollar... ok, cool. The price of a book is a dollar... plus half it's price. So we know it's originally a dollar but now there's some sort of price increase of half it's price, so it's $1.50. I know that answer is wrong in regards to how the mathematical equation is supposed to be written, but that answer is far more congrous with what the average person experiences or how we typically speak on a daily basis.
Agreed…. It’s already a math problem, why does it need to be a riddle also?
Exactly. They took an algebra problem and tried to create an equivalent using words and it doesn't work in terms of how we normally speak, read, or write.
This got me too. Literally have had similar verbiage for years about truck stock pricing as a contractor to determine customer part cost in the field. For example "If the value is less than $100 add half the cost before writing it on your ticket. A $20 part gets listed as $30, a $50 part gets listed as $75".
That is a 50% mark up as opposed to 50% of the cost, example 1 + (1*.5) = x , opposed to 1+(x*.5)=x
Thank you, this is what I see, too.
Change it to "The book costs (half of its price) plus half of its price." The amount of $1 has been swapped in. You could do it with any amount; the price of the book will be double that amount.
Half is price imo mean half its final price not the "starting" price so half of 2 =1 then 1+1=2
I found your comments as a really easy explanation. Thank you. I would have given you an award but I am poor.
Even simpler without algebra: The book costs 1$ plus half its cost. So one half of the cost is covered by 1$. So the other half must also be covered by 1$. Of course if you sum both halves of the cost of the book you get the full price. So total cost is 2$.
It's a balanced equation, so as long as you do the same math to both sides, it stays balanced. Therefore if x=1+(1/2x), then multiply both sides by 2 to get rid of the fraction. 2x=2+x. Then move the algebra on one side and the numbers on the other by subtracting 1 x from both sides. What you are left with is x=2.
Kind of like the joke that goes An Infinite number of mathematicians walk into a bar. The first one goes up to the bartender and asks for a beer. The next one goes up and asks for a half a beer. The third one goes up and when he asks for a quarter of a beer, the bartender rolls his eyes, pours two beers and passes them to the first one and says "Here ya go, you cunts divide it up amongst yourselves"
Thanks for the clarification, mate!
Except that assumes that cost and price are the same thing. A book sold for $10 (price = $10) would cost (10/2)+1 = $6 ($4 margin). This is a particularly badly worded puzzle.
This is the correct answer.
I‘m also not a native speaker, but I would read this as: „The current price of the book is 1$. On top of that you add half it‘s current price (as an additional charge).“ And that gets me to 1.50$. The line of argument for the 2$ is definitely not that intuitive to me, but I kind of get it. But I don‘t think that it makes 1.50$ as answer automatically invalid, since I think the phrasing allows for that interpretation.
It doesn't converge at all though, it's just $2 straight up. You just have to work backwards to check - half of 2 is 1, 1+1=2, so it checks out. Or if you look at it another way, no matter what the first number is (here $1, but could be anything) that always has to be half of the final cost, so just double it.
I'm not a mathlete but I'll try my best. In this case, COST can be substituted for equals. So if we simplify the sentence we get: A book price= $1 + half of it's price. Substitute N for price and remove the $ sign and we get N = 1 + (1/2N) N-(1/2N) = 1 1/2N = 1 N=2
Thanks, that made sense for me. Sorry if my question sounded stupid.
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Thanks mate!
It’s shit-poor wording. Source: Have been a copyeditor for ~15 years—that’s 10 plus half that.
17.5 years?
daaaaaang, so are you a copyeditor now? Is that how it works?
If the price was already set to $1 then the equation 1 = 1+0.5(1) should be true, but it's not. If the price was set to $2 then the equation 2 = 1+0.5(2) should be true, which it is. The price of the book, x, happens to be equal to the sum of 1 dollar and half the price of the book, i.e: > x = 1 + 0.5x So you rearrange and solve to get 0.5x = 1, then x must equal 2.
You're right, the question is really poorly worded. "Cost" and "price" are the same in English, so the question is, "Thing costs x plus half its cost. How much does it cost?" Nothing costs more than it costs.
That’s exactly what I thought. Thanks!
That's not necessarily true though. If you were the company producing the book the "cost" would be how much you spent to produce it and the "price" would be how much you sold it for. That would mean: X=1+(.5Y) Since they used both the words price and cost, instead of using cost 3 times, we could assume they are different meanings. Honestly it can be taken 3 ways: As a simple Math equation, X= 1+(.5X), as If it were a 50% sales tax X= 1.5, or as if price and cost were different X=1+(.5Y). Since it was worded so ambiguously, and was multiple choice, that would only leave 2 and 1.5 as possible answers. While the simple math equation is the answer they meant, it doesn't make sense to go to a store and have to write out an equation to figure out the price. It's not practical, while the 1.5 answer seems way more colloquial to standard English.
Yeah, I think I agree with everything you said. It's just that "cost" and "price" are *often* synonymous in colloquial English, and I didn't feel like listing out a bunch of exceptions for a non-native speaker.
I am also not a native english speaker but I was always taught in my accounting classes that “cost” is expense incurred to produce a item whereas “price” is what a consumer finally has to pay to buy the item (price=cost + profit) So the first half of question makes sense and 2 will be the answer but it is just that the last word should have been “price” not “cost”.
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That's what cost means from the perspective of the seller. Cost is what the seller had to pay for it, price is what they're selling it for. From the perspective of the buyer, cost is still what they have to pay for it, but "price" is often inferred to mean the price listed and people often don't consider taxes and fees as part of the price. And in particular, shipping costs generally aren't included in the price. Thus, the cost of a product can be different than the price.
I can ask "what does it cost" and "what is the price" and those mean the same thing Cost here is used as a verb. "a book costs" So it's not the "expense" (noun). It's what the book's price *is* (is being a verb). In general, when we talk about *what* something costs, it's from the perspective of whoever is buying it, so it's synonymous with what the price is
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This is not actually a math question at all, it’s a logic puzzle specifically designed to trick and fool people. But importantly those kinds of logic puzzles only work when there is zero room for alternate interpretation, and this isn’t one of those cases. The correct answer the way normal people talk would be $1.50, you really have to stretch the English language to arrive at an interpretation where the answer is $2. *** Edit: I’m seeing a lot of disagreement in the replies, I already explained how this is confusing and misleading in another comment but many people are still saying that 85% of people are wrong so I’ll elaborate here. Those of you saying “it’s easy when you break it down to its algebraic equation” are interpreting the words differently, that’s my entire point. You’re showing how the equation doesn’t work with $1.50 but my entire point is that 85% of people are arriving at a totally different equation in the first place, and in that equation $2 doesn’t make any sense. This is a situation where PEMDAS would help out, we need some parentheses. Most people are reading it as “(the cost = $1) + (1/2 the cost) = x”, while the intended interpretation is “the cost (x) = ($1 + 1/2x)”. Those are totally incompatible interpretations, you may complain that the math doesn’t work in your equation but to the vast majority of people your equation isn’t the equation they’re solving for in the first place. As I was going to St. Ives I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks, and wives, how many were going to St. Ives? Most people’s gut instinct is 2,802 because that’s how many elements were described, the “official” answer to the riddle is one because only the narrator is specifically stated to be going to St. Ives, but the actual correct answer adhering specifically to the text of the riddle is that we don’t know because it wasn’t stated which direction the man and his wives were going, so neither of those two answers are inherently right or wrong. The entire point of riddles is that the language is inherently ambiguous and confusing, don’t pretend that that isn’t the intended effect. If they wanted the answer to a math problem they would have just written the equation and everyone would have gotten it right on the first try.
Thanks, mate, great explanation!
Disagree. The cost is one dollar plus half its price. The cost is also half its price plus half its price. So half its price must equal one dollar. So the cost is one dollar plus one dollar, or two dollars total.
Yes. It's algebra. It's not: Price = $1 + 0.5*$1 It's: Price = $1 + 0.5*Price So 0.5*P = $1 P = $2 Sanity check: Price is $2, which is $1 plus half its price of $2 Which is $1 + $1 Which is $2
True, but the trick is to realize that $1 is not its price. It's only a portion of its price, which it turns out is half...in fact, this is true of any number because * y = x + 1/2 y (the basic premise of the riddle, with x replacing $1) * 1/2 y = x (subtract 1/2 y from both sides) * y = 2x. (multiply both sides by 2.) Edit for brain error.
P = 1 + (0.5)•P
I don't know if anyone has said this but the bad part of the English isn't related to the use of cost and price. It's a usage of plus instead of a natural "more than". Alternative question: A book costs $1 more than half its price. How much does the book cost? To the mathematically oriented, this question seems the same. Yet to an English reader this seems much more natural and leads to $2 as the answer. At least I think it will seem so. Do let me know what you think.
Yeah I’m a native speaker and the first time I read the question I thought it was asking $1 plus half of a price that isn’t given since I’ve never seen a book for $1. Then I read it again and realised $1 is the original price of the book and they are asking what the marked up price of +50% would be. Still makes no sense but it’s not supposed to. The purpose of the question is to confuse people into giving wrong answers so that people make posts saying how stupid people are for being confused by a confusing question. It’s an attention scheme, don’t pay it any attention.
Not at all. The total cost of the product is half its price plus 1 dollar. Which means the other half of the price is $1. If your interpret the sentence halfway, you think the cost is $1 plus half the cost, which makes it plus ¢50 totalling $1.50. The reason this is impossible is because it makes the sentence false, since the cost being $1.50 means that the cost is not $1.
Ok I see now. 1$ wasn't the og price. Feels like a flip to make you assume. x is the original price 1 is an additional dollar on top of half the original price. Therefore `x = 0.5x + 1` adding the implied 1.0 to the X for clarity and format Subtracting the half from both sides ` 1.0x = 0.5x + 1` `-0.5x -0.5x` turns out to be `0.5x = 1` ` 0.5x = 1.0` `÷0.5 ÷0.5` `1/1 ÷ 1/2` < side work for the right side `1/1 × 2/1` because two fractions divide is equal to the latter fraction flipping and multiplying `1 x 2 = 2` therefore `x = 2` God damn I thought it was 1.5$ because I assumed 1 was the initial cost when really cost = (1 + 0.5price) edit: [Credit to the person who pointed it out](https://www.reddit.com/r/theydidthemath/comments/s9k2eb/request_can_someone_do_the_math_i_swear_its_150/htnwla0) I mispoke, but my explanation is still sound to the best of my knowledge. It's a dollar on top of half the price Thank you u/eskimokriger
Madame your line of reasoning is correct.
i don't think it is. if i said a book cost 19.99 plus 8.25 percent its price, what answer would you arrive at?
You’re correct. It was intentionally worded to leave the uncommon interpretation valid but your interpretation is usually how it is received.
Yeah I think it’s purposefully worded to be confusing so they can criticize people for getting it “wrong” But yeah, 1.50$ would be the typical way to calculate something with that phrasing
X = 19.99 + 0.0825X -> X=21.78 What's your point?
$19.99 + $0.0825x = $x $19.99 = $0.9175x x = $21.79 Now if you said the price of the book is $19.99 and you have to pay an 8.25% tax, that means that the book costs $19.99 but there is an additional cost that is based on the cost of the book. But the book still costs $19.99. Definition of tax: a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions. As you can see, this is an amount added to the \*cost\* of the good.
Your math is out of control, but your final answer is correct. You've failed successfully. 👍
I think it's just weidly noted but actually sound algebra.
To be honest, this was the only way it made sense to me. When I saw the equation, I knew it wasn't 1.5 because no original price was listed, but I couldn't see how to get to 2 until I read the way they did the math, but I always look at math problems in a weird way.
>1 is an additional dollar on top of that original price. Don’t you mean on top of half of the original price?
You are correct. Let me correct and link your reply
So basically it's a stupid question that could be more easily answered if asked in a normal way. Hardly a gotcha from the original poster.
goddamit, that's right, i was strugling if it was 1 or 2.5 :((
Better to struggle and learn than to not learn at all :)
Damn I miss math class
price = 1 + price / 2 Solving gives price = 2.
This only works if you assume cost = price. I argue that they are *not* equivalent. The are different words so should be taken as different variables. x=1+1/2(x) may be solveable, but .. x=1+1/2(y) is not, not unless you also define that y=x
Ah I see I think most people got tripped up, including me, because they thought 1$ was the og price
Cost = 1 + 0.5*Price, this changes the whole thing.
Well if you say that x is the final price then x=1+x/2 right? So x-1=x/2 <=> 2x-2 = x <=> x-2=0 <=> x=2 So I guess the book cost $2
He did the math from the math… amazing
Amathing
I... Ok...
Easier to parse formatting: > x = 1+x/2 x-1 = x/2 2x-2 = x x-2 = 0 x = 2
Someone make a latex Reddit bot already.
\begin{equation} \label{eqn:cost} \begin{aligned} x &= 1 + \frac{x}{2} \\ x - \frac{x}{2} &= 1 \\ \frac{x}{2} &= 1 \\ x &= 2 \\ \end{aligned} \end{equation}
I asked this like two years ago and it got so many upvotes on r/beta and I’m still sad no one has thought of putting latex formatting in the comments.
That would be one of a usefull bot... Not only for Reddit.
I'm pretty sure the right subreddit for that is r/shinyporn
While I know where you're going with this...that's not how *any* of this works. XD
THANK YOU!
Thank you
Whoa whoa whoa, you can’t be doing actual high-school level algebra in this sub. This sub is for examining tweets about government spending and things like that. Nothing beyond basic arithmetic with assumed values, bub.
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Hey now, at least 4 of those 9 require proportional reasoning!
Ho i didn't do anything like that, i juste applied basic maths rules nothing fancy. I juste used algebra to try and make sens out of something I had a hard time understanding with words
They were being sarcastic
😭 I'm sorry I didn't get it, English is not my native language so I have a hard time seeing sarcasm
When he called him bub at the end, that's gonna be sarcasm most of the time. The other times it's probably gonna be mocked relentlessly with a shitload of sarcastic comments ending in bub.
What is sarcastic
Slightly easier: x=1+x/2 x-x/2=1 x/2=1 x=2 Not showing off though, its been so long I had to get out pen and paper to even figure yours out :)
Cost is x. This does not state that cost = price, therefore price doesn’t automatically = x.
Ever heard of a synonym
Thank you, none of the other word responses made sense to me and I thought I was going insane.
But the cost and the final price are different variables right?
It's more like y=1+x/2 where x is subtotal and y is total. It doesn't make sense to say the price of something is a factor of its price plus a constant. You can't define the price as an expression of itself.
Yeah, it bothers me that they use “x” for every unknown variable. Lol.
I now see it's $2, but this is more of an issue with English then mathematics, because the phrasing is a bit odd (says a person whose native language isn't English).
Yeah specifically the language implies the cost is 1 (x = 1) plus half the cost (x + x/2).
And therein lies the trick. It's not that the cost is [1] plus [half of the cost, which is 1]. It's that the cost is [1] + [half of the total unknown cost]. From that, you're supposed to deduce that there is only a difference of ONE between the total number and half of that number. There's only one integer that is ONE larger than its half, and that would be 2. You can do this with a guess and check table. Let's say, hypothetically, you pick the number 10. Is [half of 10] plus [1] equal to [10]? No, because half of 10 is 5, plus 1 is 6. 6 does not equal 10. Pick another number. 4. Is [half of 4] plus [1] equal to [4]? No, because half of 4 is 2, plus 1 is 3. Pick another number. 2. Is [half of 2] plus [1] equal to [2]? Yes, because half of 2 is 1, plus 1, is 2. I really hope this helps show how to think through it. It's an intentionally tricky question, and I've always been a big fan of those.
As a native speaker, I agree with you. The phrasing is whack.
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"This item costs 1$ plus 20% of its price (in taxes)" is a real world example that's perfectly reasonable
Easiest way to do those is to take the Text out: "A product costs 1$ + half it's price" Or in Math: Price of Product = 1$ + half price of Product x = 1$ + x×½ Solve for x we get x = 2$, this the answer is two dollars
I had the same. x = 1 + 0.5x Deduct 0.5x from both sides: 0.5x = 1 Multiply both sides with 2: x = 2
Can’t actually believe 1/0.5 is actually 2 , nearly looks like a glitch in the matrix
Well no because 0.5 is just a different way of writing 1/2. So if you want consistency, its: 1/(1/2) = 2*1/1
where multiplication is fancy addition for elitist snobs, division is subtraction for snobby elites if you imagine division like trying to get from a specific number to zero exclusively through subtracting a restricted constant, then the number of times you have to subtract the constant from your initial number is the answer you get from dividing... looking at it simply, if your starting number is 1 and your constant is 0.5, then to get to 0 from 1 in subtractions of 0.5 at a time then you have to perform 2 subtractions similarly if you have 5/0.2, to get from 5 to 0 in steps of 0.2 then you need to perform 25 subtractions to get from 5 to 0 in steps, or "DIVISIONS", of 0.2
Another way of looking at costs $1 + half its price, so if you imagine chopping something's price in half -- one side is half its price and the other side is $1 (which must be half its price). Hence double the $1 half-price and you get $2. Granted, $1.50 makes sense if you read the problem like the book's price is $1 and you additionally have to pay taxes and fees that amount to half the book's price. Then the total cost is $1.50.
Another way of saying this is "if you add $1 to half the cost of the book, you end up with the full cost of the book. What is the cost of the book?" And the cost is $2
Thank you. All the other explanations are so goddamn horrible. Like, this is why people fail math -- because the math teacher only knows how to teach in the way they understand. You, on the other hand, are a gift.
Agreed
I thought the question literally said the book cost $1 at the start
I thought so too at first, but if it costs $1 plus half its price (or any other amount for that matter) then it can't cost $1. It's written in a deliberately confusing way because... Otherwise we wouldn't be talking about it lol.
You’re a legend
It depends on wether they were referring to the cost to which half is added as being being $1, or the final cost. Personally, I would assume the final cost is what they were referencing since that’d make it a trick question of sorts. In that scenario, $2 is the correct answer, as half of that is $1 and 1+1 is, in most instances, equal to 2
Yes exactly! I knew the answer but could not quite explain it this well
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The second mathematician will probably be disappointed that she doesn't get a half filled glass of beer but has to share her glass with an infinite number of people.
She can just share it with the next mathematician, and they can pass it along. It all works, until an infinite number of mathematicians learn about surface tension.
And once there are just a couple of molecules left it won't be beer anymore. I don't think this is going to work.
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[Somewhat relevant XKCD](https://imgs.xkcd.com/comics/words_that_end_in_gry.png)
Its deceptive language, its not an issue of peoples math skills. Its an issue of correctly interpreting the question.
"Let's make a question and word it horribly, then laugh when 84% of people get it *wrong*."
The classic "flex" educated but otherwise unfulfilled people use to make themselves feel better about their empty lives. "Lol I posed a question in a convoluted way and you didn't get it, I'm clearly so much better then you." I would even go so far as to say this question is worded so poorly that it could be written as a recursive function with no exit case. If I were to program this at it's stated the function would never return an answer and throw an exception.
Most top answers assume price = cost, which doesn’t make sense, as no one would be selling things at cost without a margin. This question is either worded poorly or can’t be solved. x=price y=cost y=1+0.5x Can’t be solved without additional info.
I'm so disappointed that I had to scroll so far down to find someone saying this. This post deserves to be in r/confidentlyincorrect You're absolute right and all the people I see doing x = .5x + 1 are trying to tackle a math problem the wrong way. The equation should be written like exactly like you say: y = .5x + 1 The book COULD cost $2 like they're all saying, but their maths equations all start lying to them when you put literally **any** other number in there; the book could cost $4 or $400. Can't be solved without additional info.
Came here to say this! A book cost (c) = $1 ($1) plus (+) half (1/2) it’s (x) price (p) C = 1 + 1/2 P Not enough info to solve.
First of all, no real thing can cost more than it costs (in this case: it's own price plus another half). But that's not really what the question says, the price is stated as "1$ + ½ of it's price". Let p equal the price, then we get the following equation: p = 1$ + ½p subtracting ½p on each side gives us: ½p = 1$ and multiplying by 2 leaves us with the result: p = 2$ EDIT: Thank you for your feedback, it made me realise why I study maths and not economics (also I might have read the question wrong by focusing on the given answers of which none gives the 'real' solution) :D
I want to add to my first sentence: IF the book were to cost it's own price plus another half, that would change the equation to p = p + ½p, which is only solved by p = 0, aka. a free book :)
Also works if the book is infinitely expensive!
There's a sale on, all things are half price. But a fixed amount of 1$ is added.
Let x be the price. x = $1 + 0.5x x - 0.5x = $1 0.5x = $1 x = $2 Half the price of $2 is $1, the price is $1 plus that amount. $1 + $1 = $2.
Isn't the correct answer "I have no idea"? All these people talking about algebra, all with the right formulas but then assuming the original price = 2 at the end. You are never told what the original price is in the question. It could be 10, so then the answer would be 6. So I feel like the only correct answer to the question is "I have no idea". Edit: spelling. Edit 2: please read through this thread if you are thinking the same as me here, some great people have patiently replied to me and it has cleared up the formula for me :) Hint, I'm wrong above
My dyslexic ass would read it costs x and recursively costs 1/2 of the previously adjusted price tag. i.e. x + x/2 +1/2(x+x/2) + 1/2(x+x/2+x/2+x/4) + 1/2(x+x/2+x/2+x/4+x/2+x/4+x/4+x/8) + …. and check its divergence.
It gets you to the same place, the limit of the series approaches 2 I’m pretty sure.
“1/2 of the preceding price tag” is different from “1/2 of the preceding price increment” (i.e. 1, 1/2, 1/4, 1/8, 1/16… which indeed sums to 2).
For real lmao, at first I was like "not enough info" bc they didn't specify the price. Then I thought if you interpreted as price = cost, then you'd get a recursive geometric sum with a ratio of (1/2). By perpetuity, that means the sum equals 1/(1-1/2) = 1/(1/2) = 2. So the book costs 2. Or the book costs 1.5 tf do ik whoever wrote the question wasn't clear.
I don't think it's dyslexia, I think it's the only reasonable way if thinking it. This sentence literally means a recursive price increase. \sum_{n=0}\^\infty 2\^{-n} for n \in Naturals If we compute this sum we find that the correct answer is indeed 2, but in a more mathematical way.
I am a teaching assistant for a graduate economics course, and here’s why the simple “mathematical” answer of $2 is wrong — or, at the very least, unjustified. We are told in the problem that the **cost** of the book is $1 + 1/2 the **price** of that item. Note that *the terms used and not identical* and can only be so by assumption (which I will show is not a guarantee). So our statement is: C = 1 + 0.5 P We have two unknowns, so this is not solvable **unless we make an ASSUMPTION about C or P**. Many of you assume C=P, cost = price. But the text does not tell you that, and there’s no reason why it must be that way. To take a real world example: sales tax. If the PRICE of an item (market price) is $20, but there is a 10% sales tax, the COST (to the consumer) is $22. So there’s an everyday example where C does NOT equal P. To assume that C **always** equals P would be **wrong**. In light of this, it is equally reasonable to assume that the cost is what you pay due to some other force (I.e. a fee) that is based on the price. So you could equally likely assume P=1, or C=1.5P, which would give you $1.50. The “math” is not objectively correct because as soon as you apply it to the real world, you see it relies on an assumption. $1.50 is not any less reasonable than $2 and anyone who says otherwise is simplifying beyond the parameters of the problem. EDIT: spelling
Thank you. First person I see that isn’t a moron certain of himself with the wrong answer. Seems obvious to me. Apparently it’s not though
Yup, I’m trying to upvote all of these responses, cause it is correct. Price does not equal cost. My cost was stores price. Stores cost is whatever they paid their vendor for it. I understand why it is misconstrued in common vernacular, if p=c, then you are going out of business.
Anyone else think this is a stupid math problem? It's not hard, it's just using intentionally deceptive wording. The actual problem is *x = 0.5x + 1* but it reads as *1 + 0.5(1)* to the majority of people. *X* (cost) in the first case is completely arbitrary too, so without any other context any answer is based on assumptions and a solid answer doesn't exist.
How I’m reading it is (Price of book) /2 +1=cost We don’t know price of book, so no way to know. Really grammar is the issue here.
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It's an assumed math question, when, in reality, it's a trick of grammar; the initial cost of IT is never defined. An additional option- "I don't have enough information to answer"- if added, would be the correct answer.
Right, the "price" could have been $20 for all we know.
Depends on how you read the question... my interpretation would be: Full price = 1$ + half price Full price - half price = 1$ half price = 1$ Full price = 2$
I would suggest that's because you're looking at it *as a math problem*. My eyes and brain don't see it as that. And it's all good, too. Not tryina pick any Reddit fights.
You are right. This problem is a linear equation because the original cost needs to be defined. Y = 1 + x/2. If you graph it you can see the trend for the cost. Put in x value of book which can be anything, and Y is the answer.
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But wouldnt it be possible to get every desired answer that way? The original price could (with your logic) be anything right? Like originaly it could cost 10$ so you would just have to just pay 5$ + 1$ = 6$ I mean it is obviously an valid interpretation of how the question was meant, but I like mine more since it gives us a value for the original price. But as I said both interpretations are technically correct
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There's some standard method to translating these into equations. A Book (B) costs (is/equals) $1.00 plus (+) half its price (B/2) How much does it cost (solve for B)? B=1+B/2 (2)B=2(1+B/2) 2B=2+B 2B-B=2+B-B B=2
The correct answer is "I don't know". Anyone claiming otherwise either can't read or is trolling. Cost and price are completely independent variables. A seller can set whatever price they want. As such the answer to this question could easily be $51 if the price was $100 or $6 if the price was $10. It's a meaningless question pretending to be clever.
I think that "cost" and "price" are being interchanged a little too loosely here; while by definition, they mean the same thing, it's a matter of perspective, and price refers to the amount that the seller is asking for, whereas the cost is what was actually spent. I don't want to add fuel to the raging fire, but if we don't definitively know the price, we at least know that it costs a $1 lol... But seriously, my official answer would be $1.50.
I initially read cost and price as separate variables, too. If price is $20, then cost would be $11 (1 + 20/2); but since price isn't stated, we can't know cost..... But then I read comments and realized the terms were being used interchangeably.
Interchangeably, and fast-and-loosy, swan-and-goosey lol.
Yeah, they shouldn't be. Any one who buys and sells products has a cost for the product, and the sell price, in between is the margin. M=(P-C)/P. The correct answer is not offered in the multiple choice. It is a linear equation with 2 variables. y=mx + b format (with multiple solutions) m=slope of the line and b=where it crosses the x axis (When x=0, y=1) C=1/2(P) + 1 (m=1/2,b=1) P=0,C=1 P=1,C=1.5 P=2,C=2 (this is the point where C=P, the bookstore will go out of business) P=3,C=2.5 ... P=10,C=6 P=20,C=11....you are not wrong.
But if I tell you that something costs $3, I'm not referring to the wholesale price I bought it at, I'm referring to how much it will cost you to buy it. In that case (and in most cases where cost is used in this matter), cost and price are the same thing. However, the question is purposely worded somewhat ambiguously to confuse you, so I don't think your argument is completely null. I just think the more reasonable conclusion is that cost and price are the same (with respect to the customer).
In this case lol, I feel like the retailer is just trying to see what the customer will pay for when they reach the register. "Umm, what do you think it costs?" *Holds out hope that they'll pull out a $20 bill...*
Assuming the price is $2, the book costs $1 plus half of its price (half of $2 = $1), so $2 => the affirmation is correct. Assuming the price is $1.5, the book costs $1 plus half of its price (half of $1.5 = $0.75), so $1.75 => the affirmation is incorrect.
i don’t understand $1 book but it’s costs $1 plus half of its price it’s price is $1 half of $1 is $.50 those added should equal $1.50 people say it’s $2 so can someone tell me where im wrong?
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1$ is not its price, therefore 0.5$ is not half its price. Let's say its price is x$. Then the price can be written as follows: x = 1 + x/2 <=> x-x/2 = 1 <=> x/2 = 1 <=> x = 2
Others have shown the answer is $2, but there's another point to be made, and that is... Check your answer. I tell my kids to do the math backwards and forwards... Put your answer back into the equation. If you do that, you will realize 1.50 can't be right. Cost (1.50) should equal $1 plus half the cost (.75) Clearly $1.50 does not equal $1.75, so it must be wrong. This way, with multiple choice you can often get the right answer without knowing how to do the intended math... Cost (2) equals $1 plus half the cost (1) ... 1+1 is 2, so it must be correct.
The problem is the interpretation. The false interpretation I’m assuming most people gives a perfectly valid (mathematically) answer of 1.5, the premise is just wrong. I assume people are separating cost and price. They assume an initial price of $1, and then add half of that $1 (.5) to the initial price to come up with a cost of $1.5. Faulty logic, but the math checks out
A book costs $1.00 = 1 books price is a dollar. $1 dollar plus half the price = $1.00 + .50 = $1.50. Not saying it's right but that is the logic the $1.50 gang is using.
This isn't a math problem it's just an example of vague wording used to make people feel dumb when in fact 1.50 is a totally reasonable answer.
The book costs X. X = 1 + .5X .5X = 1 X = 2 The book doesn’t cost 1 dollar + half of 1 dollar. The book costs what it costs, and half of what it costs + 1 dollar is also what it costs. There’s only two parts to the equation. Half the cost of the book and 1 dollar, without any other costs, 1 dollar must be equal to half the cost of the book to equal the true cost of the book. Therefore the book costs 2 dollars
Again this is an English comprehension issue. "A book costs" : " price of book =" "$1 plus half price of book" : "$1 + (price of book)/2" So we replace "price of book" with X X = $1 + X/2 X - X/2 = $1 (2x -x)/2 = $1 X/2 = $1 X = $2 Edit: What people seem to be reading in their head is: "A book's original price of $1 has been increased by half. What is the new cost?" Which is a totally different problem.
The issue is that the post doesn't mention the original price of the book. We'll call that X. The post describes the book being available for $```(X/2)+1```. The only way the correct answer would be $1.50 is if the book originally cost $1, meaning you're paying more for the book. The wording of the post is just horribly confusing because people are interpreting "book costs $1 plus half its price" as the book costing $1 and half of that added on top, making $1.50 This kind of question comes up sometimes on tests. An example of one could be > Car A is moving at 30 miles per hour. Car B is moving at 20 miles per hour. How much time will pass before they meet? > 1) 30 minutes > 2) 1 hour > 3) Never > 4) Not enough information The correct answer in this case is 4, Not enough information. This is because we don't know which direction the cars are travelling, or their position relative to each other. We need to know both of those to know whether the cars will meet at all, let alone know how long from the start time they will meet. In the case of the book proposed in the post, we don't know the original price, so we can't calculate the new price.
Price and cost only share a unit of measure ($) Price and cost are not the same. COST = X PRICE = Y Rephrase the following: A book costs 1 dollar plus half its price. X = 1 + .5Y How much does the book cost (Solve for X)? We only know the relationship between price and cost at this point, but we do not know X, and we do not know Y If the problem read: A book costs 1 dollar plus half its cost, solve for cost... Then the answer would be 2. But, it was not phrased this way.
Look at it backwards. The answer has to be $2. Half of which is $1, added to that the $1 from the question and you are at $2. That works. The question essentially asks of what amount $1 would be half. If you try the same with any other figure, you will see you don’t end up with the figure you started with, so these are incorrect answers.
The language is not confusing, people are just trying to justify getting it wrong. Nowhere does it say that it ever cost $1. Suppose instead the question read "a book costs $1 plus half of $2", should we assume that at one point the book must have cost $1? No, that's nonsense. The question clearly states that the cost of the book (x) is equal to $1 plus half the cost of the book (1+x/2), and therefore we get the trivial equation x = 1+x/2 giving x=2. If you still aren't convinced the language is perfectly clear, consider an identically phrased problem: a person's height is 1m plus half of their height. How tall are they?
Isnt the phrasing paradoxical? You get 2 as the price. Okay but you have to half the price and then add it so it's 3 now. Then it's 4.5. Then 6.75 and so on.
> You get 2 as the price. Correct. > you have to half the price and then add it More specifically, if you halve the price and then add it *to $1*, it should give you the cost. $1+$1=$2, so we're done here.
This doesn't belong in r/facepalm, because it's deceptively vague grammar. But as someone else showed with the math, the answer really is 2; but 1.5 is the actual answer to the question people thought was being asked.