Can you solve the puzzle that's dividing the internet?
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- เผยแพร่เมื่อ 27 ก.ค. 2024
- What's the answer? A book costs $1 plus half its price. How much does it cost? Nearly 40% of people are not able to solve for the answer.
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I think people said it can't be answered because of recursion, rather than price vs cost. Starting with $1, the price becomes $1.50. But half of that is 0.75, so the price becomes $1.75. But half of that is 0.88, so it becomes $1.88. And then they give up.
1 + the sum of 1/(2^n) as n goes to infinity
An infinite number of mathematicians walk into a bar. The first says, I'll have one pint of beer please. The second says, I'll have half a pint of beer please. The third says, I'll have a quarter pint please. The fourth asks for 1/8th pint. Etc.
The barman pours two pints and says "you guys really ought to know your limits"
@@plotted_pant42 Which, luckily enough, converges at 2 (which is also the actual answer).
@@Stratelier Because of the semantic confusion, i have trouble determining whether or not this is a coincidence
@@xereetoAfter a good drink they all return to their infinite hotel, but the recepcionist says infinitely many new guests have arrived and everyone needs to move into a new room.
If the book costs $1 plus one half its price, then $1 must be the other half. So the book costs 2 × $1, or $2.
that is the correct logic for this.
@@GraveUypo That's definitely how I found the answer.
Exactly 💯
Noice! 👍
That actually helps a lot for me understanding this. Originally I was confused and got the wrong answer, because I was like "well you could set the price to anything you want, so telling me it's half the price +1 doesn't tell me much" but this clears that up.
Seen it in other wording in another soviet math puzzles book: "A brick weighs half a kilo and half a brick. How much does a brick weigh?". The puzzle itself must be even older than that, because someone had to know it before putting into the book.
Yeah this is a much better wording.
It seems like a lot of the controversy of these viral internet questions stems from them being poorly worded. I understood this one much better.
Wait, this video is over 8 minutes long. Really curious how that question is going to get stretched.
Taking very slowly with weird long pauses between each sentence. I had to watch 1.5x
@@OmnipotentO You should have watched at 2x, 1.5 is the wrong answer.
@@FlyingFox86 LOL
@@FlyingFox86 haha, very clever
NEED THE 8 MINS 🤑🤑🤑🤑
Working backwards from the answer.. it's much easier to see what the question is actually asking. The answer is actually right there in the question. "one dollar plus half the cost" -- literally implies that the $1 is the 'other half of the cost.
Thats a good way to look at it
I had the same thought! Honestly, internet just loves to argue over the dumbest things.
Yeah I thought the price and cost were 2 different variables, and that the $1 was an additional fee not factored into the price, it's a poorly phrased question. im so used to hidden fees in capitalism I thought thats what it was
But it is not correct. Price= sticker price. Cost = what you pay.
@@charlesspringer4709 In a world with taxes.. You're right.
I think you missed the biggest possibility of why people were choosing "the value cannot be determined". In your presented formula of b = 1 + b/2, you make the assumption that price and cost are not only interchangeable but are in fact equal to each other. Other people are seeing those as two different variables, meaning they are trying to solve the equation as c = 1 + p/2, where c is the calculated Cost of the book and p is the *known* Price of the book. In that situation, the problem does not present enough information to solve as both c and p are unknown values.
You just gave an example of someone who overthinks the problem!!
We are clearly meant to assume they are equal
It is so easy to determine that half of a book's price is equal to half of the damn book's price. The reason why the whole and half are in the equation is for you to be able to solve the damn problem. Those who make 2 different variables obviously forgot how and when should you use these variables. We have variable b to account for the WHOLE price, and the half of the price was mentioned so that would be the half of b. It is not an assumption made by this TH-camr but it is an obvious rule in solving algebraic expressions that when you have a given and half a given then they'd of course correspond and be b and b/2
Some of this depends on your life experience. Many will just assume (remember the 'when you assume you make an ass out of you and me') that price and cost are the same thing...but anyone with business experience KNOWS that price and cost are NEVER the same thing so you have an unknown variable in the question that cannot be answered. You can't say that this thinking is wrong...because technically it is MORE correct than assuming that cost and price are equal despite them being synonyms in the dictionary.
@@recoilrob324 the price of a book is the cost of a book if you are buying it, sure for a corporation there’s a difference, shipping, tax, storage, and other things must be considered, but for a consumer it’s not two different things
Regarding the cost vs price thing, I would add that cost meaning price isn't just via usage or peculiarities of definition, but rather a matter of perspective. The cost of a book to create, and the cost for me to acquire it. The cost for me to acquire the already made book would be the price of the book. The book cost me $2. That was the cost _to me_ . Here, cost and price, which are themselves different things, come into alignment.
The cost to me is the price of the book.
From the perspective of the publisher, the cost will be different. (rights, price of printing, marketing, etc...)
From the perspective of the printer, the cost will be different. (materials, labor, machinery, etc...)
From the perspective of the writer, the cost will be different. (time, living expenses while writing, payables for research, failed marriage, etc...)
etc...
The fact that cost and price are nuanced but that the seller intended a more generic meaning of the word means that it is a poorly worded question. The reader cannot, without context, be expected to ignore what they know about cost and price and reliably use the intended definition.
I would say in most places, the price is $2 but the cost to you is $2 + tax…
The problem is that a book has three values attached that are commonly referred to as its cost. Its actual retail price, its MSRP (manufacturer suggested retail price), and its COGS (cost of goods sold, what they paid to acquire it).
Without specifying which if these three prices is referred to, there is not enough information in the question.
Illustrating this, the video simplifies the statement to x=1+x/2, but that only applies if we make the assumption that cost refers to its actual retail price, otherwise saying x=y in y=1+x/2 is not justified
If you speak English you should be able to understand what the question is trying to ask you. It’s not a trick question
@@koibubbles3302 You're specifically trained in mathematics to look for situations where you do not have enough information.
@@shadeblackwolf1508 overinterpreting the wording of a question is not mathematical in nature
@@shadeblackwolf1508 you could just as easily argue that “it” wasn’t defined, and that this ambiguous entity prevents you from answering the question. You have to learn how to make reasonable assumptions, so long as you’re open to the possibility that the assumption you made was wrong. If you can’t do that, that’s on you. Not the question.
It can be true that the question came from an old textbook, AND that the question was written to be confusing. There's a reason it was written in this way, and not "What is 1 + 0.5*2". To confuse people.
That's not what the people meant by confusing. They clearly stated that "the value cannot be determined".
Well, if you translate the original russian puzzle word for word it says "За книгу заплатили 1 рубль плюс ещё половину цены" which means "They paid 1 ruble plus another half of its price". So, even the author of the original puzzle meant it differently. I do think that this translation isn't only inaccurate but nonsensical, too.
I read it from the view of the seller that bought a book for $1 and wants to resell it but wants to have a profit margin of 50%. So the answer would be $1.50 in this case
Yeah, well that's wrong... so there's that.
@@johnnynick6179💀
I understand the answer in terms of how you are asking the question but I can also see how some answers were "the value cannot be determined". It you take the question to ask A book costs ($1 + (1/2Price of Book)) the price of the book may be $10, in which case the buyer is getting a deal by paying $6.00. In this case the value for the cost of the book could not be determined as asked by the question. I think the question could be considered semantically ambiguous.
Exactly.
The book costs $1.
Plus half of it's price.
Cost = Price
Cost of book = $1
1/2 cost = $0.5
Cost + 1/2 price = $1.5
Plus half it's price
Half it's price = $0.75
Cost + 1/2 price = $2.25
Cost of book = $2.25
Cost + 1/2 price = $ 3.375
Cost + 1/2 price = $ 5.0625
Cost + 1/2 price = $ 7.59375
Etc
Etc
Cost = $ infinite
Thank you for demonstrating the absurdity of the question. It doesn't work logically in English without going round in circles
There's no comma, so the phrase is 1 plus 1/2 the price is the cost. 2 is the only possible answer.
I think part of the problem is that the question sounds like nonsense. It could have something to do with the wording, alternating between price and cost. It almost makes it sound like those are two different things, like the cost to produce it versus the price to buy it.
Kind of dependent on how you define price and cost. To an end consumer, they're more or less the same thing. "The price is $2, so it costs me $2 to buy it." Not necessarily the case for someone along the chain of its manufacture.
And that's just the way it's defined in my part of the US. I would absolutely believe that there are places in the English-speaking world where the local vernacular draws a hard line between "price" and "cost".
It reads perfectly well. The problem is that literacy is on the sharp decline.
It reads perfectly fine to a 3rd grader for the answer given, to a college educated CPA, it also reads fine, resulting in a different answer.
@@ianmalcolm2552 The 3rd grader has more common sense. The problem is wrote specifically, and the mixing up of definitions could only be done by someone in finance... Charlatans of logic.
@aperinich, do a search on “cost vs price” you’ll be enlightened.
The irritating thing about word problems is when you have to make an educated guess because of ambiguity in the wording that may or may not be deliberate. While I came up with the majority answer, to a businessman the difference between the cost of something and its price is the profit margin.
If a merchant purchases something (the cost) for resale (the price) and wants to make a profit margin of 20%, you multiply the cost x 1.25. The formula for the establishing the selling price of something that costs a given amount is to multiply the cost x 1/(1-M). M is the profit margin expressed as a decimal. Thus, in the example given above, the cost is multiplied by (1/1-.2) = 1/.8 =10/8 = 5/4 =1.25. The profit margin is defined to be what percentage of the SELLING PRICE is your profit.
THE COST (as a noun) is never used in the riddle. "How much does it cost?" cost is also a verb here and therefore can't be confused with the cost of producing it.
Just like: How much does it weigh? - > does weigh = verb
What is its weight? - > weight = noun
1. A book costs something. How much does the book cost?
2. A book costs (half its price). How much does the boom cost?
3. A book costs (half its price plus half its price). How much does the book cost?
4. A book costs (something plus half its price). How much does the book cost?
5. A book costs ($1 plus half its price). How much does the book cost?
6. A book costs ($2 off plus half its price). How much does the book cost?
General form of the equation
c = book costs something
costs and price are synonyms.
x = something
c = x + c/2
Substituting for x, for
1. c = x
2. c = c/2
3. c = c/2 + c/2
4. c = x + c/2
5. c = 1 + c/2
6. c = -2 + c/2
We end up with absurdities if x is equal to or less than 0.
Either c = c/2 (where x = 0) or the "discount" doubles.
While it's a reasonable assumption that costs is a transitive verb, costs and price are synonyms, its not the only reasonable assumption. Other reasonable assumptions, are price is one part of how much a book costs, other parts (from the consumer POV) being taxes and fees, additional discounts.
While the intended answer is $2, the way the problem is formed ignores basic realities of how commerce is conducted and what things add to or subtract from the price/cost of an item, or even that something could be on sale, i.e. 2 for 1 (1 item costs half its price), or a 50% off sale (half its price).
There's simply not enough information to know if
1) $1 is in addition to half its (unknown) price; or
2) $1 is the cost/price of the book and half its price is the sales tax, resulting in $1.50; or
3) $1 plus half its price/cost (c = 1 + c/2), resulting in $2; or
4) the book costs $1, full stop, the additional half its price is meaningless, its not asking for the total cost, price + taxes + fees + discounts. Only the cost of the book.
The above is no more overthinking it, than grammar lessons on transitive verbs and cost/price as synonyms to dismiss cost and price being two different things.
It's free!
Someone has taken overthinking this problem to a level I didn't want to even consider as soon as I saw how long the comment was!! 🙄
@@michaeldeierhoi4096it wasn't overthinking anymore than the videos overthinking to dismiss cost v. price.
The short version: how much something costs includes, but is not limited to its price, taxes, discounts, fees, gratuities, and shipping.
Does the book cost $1 (price) plus half its price (a 50% tax)?
Does the book cost $1 (fee) plus half its price (a 50% discount)?
Does cost = price? Does cost ≠ price?
The only thing that you can say for certain is that the cost of the book is $1 more than half its (unknown) price.
@@ForExample2023 To each his own.
"There's simply not enough information to know if ... $1 is in addition to half its (unknown) price"
1$ 'PLUS' half it's price. If plus does not mean addition for you, then maybe you should give up doing mathematics altogether. Also, discount plus half-price does not equal end-price.
If you have to resort to a dictionary and parsing the language of the question, you're probably going about it wrong.
I'm having the problem that I'm thinking this in terms of a real-world situation or more like a developer mind-set, where a bookstore is selling a book with price X, as X / 2 + $1, where X is definitely not a value that can be determined because it could be anything. Your solution implies a "calculation of the starting price of a book" let's say, where my starting point is that "the book has already a price, but I'm selling it at half its price plus $1".
The difference is something like:
Value = 1 + Value / 2
Versus:
NewValue = 1 + OldValue / 2
And I'm blaming the phrasing of the problem (?
Ask an accountant, they will say that you are absolutely correct 👍
I'm also damaged from too many math lectures and started to find the limit to a series: b = 1 + 1/2 + 3/4 + 5/8 + ...
I'm also damaged by programming all day. My brain thinks that an equals sign after (or before) a variable must mean that it's declaring the value of the variable, rather than it just being a regular boolean operation, where we have to figure out what b is.
My brain goes to overhearing a conversation, where you missed part of it.
Person A: I bought the book at half price.
Person B: Oh? I missed the sale, so I paid a dollar more than that.
You: How much should I expect to pay for the book myself?
The problem with most coding syntax is that equality and assignment are conflated. In Java x=1 means x is assigned the value of 1. It does not assert equality between x and 1 merely declare it so.
4:52 I have this book, but it cost more than $2.
😆
Must be inflation or something
tbh i would buy one, i like really simple puzzles
My dad had it when I was a kid
I bought this book when it was $2…now it’s $1…this seems more like a vocab test…I see less math here and more word play…
It’s a simple example of x = x/2 + 1
Subtract x/2 from both sides for x/2 = 1 and multiply both sides by 2 for x = 2.
There's probably a large capture of "just show me the answer" people in the "can't be determined" option.
0:14 easy, E (it is a value that approaches infinity over time)
who liked?
$1 can be interpreted as a fee based on this wording. For example, Ticket Master has a particular event on sale for half off. When you check out, there's TM's $1 fee + the sale price of the ticket. We don't know the non-sale price of the event, therefore we don't know what the final checkout price will be based on the question.
Did you record with a $2 microphone for this specific video? Why is your audio so different in this one?
Oh mate. I listened all the way through, but even after that we disagree on that 'indeterminate value' thing. I'm with those who say "Yup, the cost is $1 plus half the price, but as you've not specified the price, the end result is indeterminable." :)
But how can the price be anything else than $2? If it is anything else, then $1 wouldn't be half of it.
@@FlyingFox86 Nope, to me! The actual PRICE could be 2 cents. Then the COST would be $1 plus (2 cents)/2. I don't see that we have any way of knowing the 'answer' from the info given unless we accept his argument that the price == cost, which is not a given here. Happy to be shown wrong, but this one may run and run!
@@BytebroUK When you want to know the price of something in a shop, don't you ever use the phrase "how much does it cost?"
@@FlyingFox86 I have rarely heard anyone in a store ever asking "What is the price of X?" instead of "What does X cost?". And when they ask the latter, no one misunderstands and instead gets into a pedantic lecture of the difference of "cost" versus "price". In fact, whenever someone does use "cost" that way, they almost always specify that they aren't using "cost" as a synonym for "price" because it's recognized that in common usage the two are synonyms. Anyone who smugly goes on about them being different in an everyday context is just being an ass.
It says "half *its* price". Not "half *the*price". A subtle, but important difference. As a result, there's no unknown: it is written that $1 is one half of its price and you need to find the total price.
So the origin of confusion is most probably a translation inaccuracy? Because the original wording did not mention price, only cost (both verb and noun):
За книгу заплатили 1 рубль и еще половину стоимости книги. Сколько стоит книга?
For the book was paid 1 rouble and half of the book's cost more. How much does the book cost?
Did you make the music that plays at the end of your videos? Is it, like, your theme song or something? Because I was very surprised when I heard the MindYourDecisions theme song in some training videos the company I work at had me watch that were definitely not related to MindYourDecisions.
It takes until 1:10 to explain the correct solution. What is the rest of the video for?
The equation you used at the beginning is not correct.
If the book cost $1 plus half its cost, then the problem should be written that way. It is not.
ergo: cost = 1 + (price/2)
Even using your own logic, let's say the book is priced at $10, the cost of the book is $6, ergo, the cost is still less than the price.
Arbitrarily saying cost=price is no different to saying cost = 10 or price = 20 or any other arbitrary values.
And even if we presume price and cost are interchangeable terms, it's not impossible to presume that the price is the price plus some additional amount (perhaps tax, shipping, or whatever) that amounts to half again the price, as presented in this example.
If a book is priced/costed at $1 plus tax (some fraction of its price, arbitrarily half in the word problem), then the book costs $1.50 for the purposes of the word problem when read as printed.
The entire problem could be disambiguated and solve the issue. There's no reason to assume cost = price when we're told cost = 1 + (price/2)
This is like complaining to a physics teacher why they aren't accounting for air resistance.
@@baldwinplayz268 No, the cost is the object, and the price is the subject, I think. They're functionally two different thing the way the sentence is written.
the question is worded confusingly, but the original answer was meant to be 2 because it was meant to be interpreted as x = 1 + x/2. x is the actual price and its value is 1 + half of the actual price, which is also 1. his equation is not incorrect
That's why the book is free!
He quite literally addresses this IN THE VIDEO. Did you even watch to the end?
But regardless of that, I think this is an incredibly silly objection. Imagine someone said "The distance between X and Y is 12m, and the distance between Y and Z is 18m. Assuming X, Y, and Z all lie on a line with Y in the middle, what is the length between X and Z?" and someone responded by saying that the question is impossible because "distance" is not the same word as "length." Any sane person reading this would understand that they both mean the same thing in this context, and although someone COULD define them differently (e.g. straight-line distance versus geodesic length), they should be interpreted the same in this question.
I have to point out that in the question, the word "cost" is used as a verb in both instances. Not once does the question even reference the cost (noun) of the book so the argument of cost vs price makes even less sense. I solved this problem the same way you did but I did the times 2 first then subtracted B from both sides. Still gave me B=2.
I'm glad I wasn't the only one confused about his little speech about the various meanings of 'cost' (the noun) when it doesn't even appear anywhere in the question.
Hallelujah, I found my peers. I was utterly shocked to see that NOBODY in the comment section seemed to have noticed that. But here we are shaking our heads at their ignorance and Presh's mistake. Greetings from a non-native speaker from 🇩🇪
I'm curious to know whether the Russian version uses the same word for price/cost or not!
"За книгу заплатили 1₽ плюс ещё половину цены"-"They paid 1₽ plus another half of its price." That is the true to the original translation
The Moscow Puzzles! I knew I've seen this puzzle before. I still own it. Lovely book, an absolute classic. Highly recommended. 😊
If A=B+A and B=A+C, then which variables can have their values determined, if any.
Please make a video on this.
a: -1/1
B: 0
C: opposite of A
in fact, that works with literally any number
@@Safetyswitch Replace the ones in a's value with variables and you are 100% correct!😀
I don't think there is much of a video to be made about that. B=0 and A=-C
Unless I'm missing something.
A-A=B+A-A` B=0` A+C=0` A=-C` C=-A
you can simply solve that with a mathematical equation too!
let the original cost be x
so the cost is 1 dollar and half of its price that is
1+ 1/2 x= x
multiplying it by 2 we get,
2+ x= 2x
by further solving we can get x= 2 dollars.
I usually solve these types of things by the equation method which makes things a lot easier than solving it by the riddle or comprehension method, as we can visualize the situation on a paper not virtually in our brain.
tranlated from russian and you're assuming it was translated correctly? why would they use two different words to mean the same thing - concept (if i understand the argument right) . why not just use the same word?
your math and answer is right given your assumption, but not if otherwise.
There is another possible rationale for "the value cannot be determined"; not that I agree with it but here it goes: on one hand it says "the book costs $1" but it also says that "the book costs $1 plus half its price" which is a contradiction so the price is not properly stated. This is actually what happens when people reply $1.5 but for some reason they don't notice it. If they get to $1.5 it's because they took price=$1 as truth but if then they add the half of $1, which means they didn't notice that they were taking two contradicting truths at the same time. Source: it happened to me when I read this problem as a kid.
If the price of the book is listed as $12 and the store is having a sale for $1+half listed price, that would be $7.
The original question is ambiguous.
$2, ez, you just lost a customer, and I saved 8 minutes of my time
Can't the cost grow towards infinity due to the cost being > 1 during all iterations of the calculation?
If you want to write it as a sum limit gotta be: infinity E(x) 0 of 1/x^2 which is 2
As is often the case, the language gets in the way of understanding the math problem. Price can mean sticker price, the original price of the book, while cost can mean the value the buyer pays after applying the math rules put in place. Imagine a book with an original sticker price of $10. If the bookstore had a sale in which the book "costs $1 plus half its price" that would come to $6. The prompt might be better phrased as "A book's price is $1 plus half its price."
This question has 3 correct answers depending on your job/perspective - and THAT is why its interesting.
Mathematician: 2
Accountant: 1.50 (and the .50 is TAX)
Engineer/Coder: Edge Case - recursive error, potential infinite recursion.
Its a genuinely interesting question, I was one of those folks that ticked the 'cannot be defined' choice (in the recent poll), because from an engineering and coding solution you are looking at a variable that is defined as a formula of itself: ie it is recursive, Ie the cost is approaching infinity - and a definition of a variable such as this is something to keep an eye out for as it is a known source of bugs. For me to get the same answer as a mathematician the question would have to specify the COST as being DIFFERENT from the ORIGINAL COST, ie the 2 variables would have to have different names. I completely understand the mathematicians perspective on this - Im just here to point out its not the only valid one.
While all 3 jobs are reliant on maths, we all all interpret certain things differently - and that is correct for our different professions, because each profession comes with certain standards and expectations.
In my career this is a prime example of something I would HAVE TO DOUBLE CHECK with the client, to make sure Im getting the correct formula and calculation, and in most real world cases - the answer would be 1.50 as intended by said client, because they exist in a world of business and accounts.
Well the coder should have studied more math because the recursion he would code, would be an infinite recursion but the "final" value would funnily enough be 2. It would be a geometric series which does equal to 2.
@@TheJinjitsu nope I see where your coming from but nope - look at it from a maths 'series' recursion yes, trends to 2... in code It trends to infinity, but much more importantly its an infinite recursion.. ie a 'crash',
I thought it was $1.50 because the book cost is $1 + half its price (0.50), but see I'm wrong.
If its prices is 1 its prices isnt 1.5 because 1 is Not 1.5
I got the same answer as you, $1 + 50% = $1.50
it costs $2 because 1+x=y with x=0.5 y and y beeing the price whole price (=1+ price/2). so y-1=0.5 y --> 0.5 y = x = 1
@@marks.9448but we assumed that $1 was it's base price and you have to pay an additional 50% of it's base price. Imagine it like you have a tax rate of 50%
@@zekiz774 if its price was $1 it would cost $1 and not $1 + 0.5 $1. and in civilised countries taxes are included in prices
A small thing but in the previous poll the sample size was 81K and the in the latter one it was 38K. So while looking at the percentages it would seem like there is some improvement, a single percent for the latter poll is less number of people that that for the previous poll. But I understand we can't always have ideal situations and we have to make do with what we have.
The only way this question sort of makes sense is that books often come with a permanent price printed on the front or back cover. A customer is at a used book store and asks the clerk how much the book costs and is told “The book costs $1 plus half its price.” Otherwise, why make a distinction between cost and price? Since the marked price is never given here, the answer is undeterminable with information given. This is a nonsensical way of stating the cost/price of an item. How much does this car cost? The used car dealer replies “The car costs $5,000 plus half its cost.” The customer immediately leaves.
I just think the sentence was translated into English and we should check the Russian that is for sure more clear... up to then for me this question is non sensical. Still interesting to see how a mathematical approach handles it.
On first though I was duh easy 1,5$. But when you wrote down the formula: b=1+b/2 it all made sense and ofc its 2$.
1.5 not 1,5
Speak English
@Emile.gorgonZola why are you so mad about a simple mistake like that 😭
Please ignore the commenter above and continue to use the decimal comma. I wish I was brave enough to stand up to the decimal point supremacists!
@@FlyingFox86Decimal comma on top
@@Emile.gorgonZolayou do realize in most of Europe they use , over .
I thought this was a trick question and I thought it was one.
The question literally says the book costs 1 dollar. (in present tense) and even though it says plus one half, that one half could be 66.6c + 33.3c = 1$.
From the Oxford English dictionary:
price /prīs/
noun
1. The amount as of money or goods, asked for or given in exchange for something else.
*2. The cost at which something is obtained.*
_"believes that the price of success is hard work."_
3. The cost of bribing someone.
_"maintained that every person has a price."_
The price is, unambiguously, what the book costs. Anyone digging into technicalities about what the cost to the seller was, or sales tax that might have been added onto the price, or any number of other things that introduce ambiguity where it was CLEARLY not intended by the writer, is drastically overthinking things.
I got the two dollar answer. Having looked at the wording more closely, I believe that the indeterminable answer is correct. The way the different words are used could easily denote a difference between the words 'cost' and 'price' rather than those words being interchangeable.
Finally someone with common sense.
I learned it as a kid like this: a hare weighs 10 pounds plus half its weight. What is the hare's total weight?
No price vs costs issue.
Oh, I know this one. The hare is a butcher. He weighs MEAT.
I thought the "cannot be determined" explanation was simply going to be that they thought we did not have enough information to find the correct answer. Boy was I here for a treat.
Assuming straight math, the answer is pretty obviously $2.
X = X/2 + X/2
X = X/2 + 1
X/2 = 1
X = 1 + 1
X = 2
The thing is, that second step assumes that the book is being sold for its normal price. If a special deal is going on, it would be something like
Y = X/2 + 1
And now we no longer have a way to determine X, and per extension no way to determine Y, at least not with the given information. If we say that the normal price of the book is 4$, for example, that means that the current price is
Y = X/2 + 1
X = 4
X/2 = 2
Y = 2 + 1
Y = 3
TL;DR: If we assume a straight math question, the answer is 2. If we apply real world situations, the answer is "too little information." Which is the major downfall when trying to make a math question into a story; the moment you make it into a real-world situation, people are going to apply real-world logic to it.
As a non-english speaker, I did not get that "A book costs $1" as its production cost, but as "A book sells at $1". Therefore I got heavily confused by the question as I was reading:
"A book sells at $1 plus half its price. How much does it sells at".
I fell in the "The value cannot be determined". Even with the equation you provided, I was like: "nope I disagree", until I understood that not only "to cost" can refer to "the production cost", but it was actually the most common interpretation!
😅
I read it this way: A book costs "the price" plus half of "the price". The wording made me read it in this way. Only when I did this: "A book costs: $1 plus half its price.", I was able to understand what the author of this puzzle meant.
I think the problem with so many people getting $1.5 is because its money, we immediately think “it was $1, but the store had to increased the price by 50%” which then comes out to $1.50, correct?
I think because it’s money I automatically changed the wording for it in my head.
I kept getting $1.5 when thinking about it myself until I saw someone who changed it to “a brick weighs 1 pound…” and then it made sense
It's a matter of people not understanding how to think, speak or read properly.
In the question, "price" is a noun, and "cost" is a verb. Referring to something's price (noun) entails the possessive form, but referring to what it costs (verb) doesn't. Writing it in this way, with the noun "price" to mean what something costs to purchase, and the verb "cost" to mean its purchase price, just sounds less stilted. Consider the alternatives:
"The price of a book is $1 plus half its price. What is the price of the book?"
"A book costs $1 plus half of how much it costs. How much does the book cost?"
People don't repeat phrases like that, when speaking nor writing. They look for other words to convey the same meaning. Thus, the "cost vs. price" distraction is born.
Look at from the perspective of a bookstore. The bookstore buys a book _at cost._ It sells a book _at price._ So _c = 1 + 1/2 p._ So we have a function of cost and price. If the book is sold at $2 the bookstore breaks even. That's all. The extra cost for the bookstore due to the higher price might be royalty due to the author, for instance.
I don't know how anyone can argue with this. Cost is not always price, depending on context, and this makes the question ambiguous and unanswerable.
If the “plus half its cost” is considered a tax of 50%, the total price is $1.50. The book costs $1 plus tax, the tax is 50%. You would never calculate the 50% after adding the 50%.
If the tax is 50%, the base price is the same as the tax, therefore price cannot be 1.50
the true answer is that the statement is too ambigious and poorly worded
Based on how people are acting the statement is crystal clear without any ambiguity
It sounded like this was an infinite recursive result. $2 seems so weird so an answer. I still don’t get the solution, but I will yield to your expertise.
When you did you subtracted b/2 from both sides, how does b-b/2 = b/2. I don’t understand. Could you clarify so I understand?
As a word problem, it’s not *fully* constrained (cost vs price), but assuming that they are used interchangeably, before sales tax or VAT, $2
How on Earth are people having problems with "An object costs X plus half it's price. What is its price?"
"I'm never going to use this"
Because people misinterpret it. Kinda like a reverse offer, where instead of 30% off, it is the cost (£1), plus 50% of the price (50p), or 50% on top. Obviously it is £2 but I'm surprised this reasoning wasn't covered. Also monetization etc.
Because, if cost and price means the same, then that might mean X + X/2, which would be 1.5 in this case. IE difference between the whole price vs just price. IE an object costs $1 and half of that ($0.5).
We're so used to trick math questions on the internet that people are looking for the trick. If you're not expecting a trick, assuming price and cost are the same thing makes sense, but if you're looking for a trick, that's an obvious one.
I don't know how people are having problems with this.
In the absense of compelling reasons to take a contrary view, questions like this should be read with the assumption that the question provides sufficient information with which to answer it. Therefore if you have a choice as to how to interpret the question, you should choose the interpretation which allows the question to be answered, rather than the interpretation which introduces an unknown. This is especially true when the first interpretation involves plain language reather than strictly technical definitions. I will go further and say that it is impossible to reason with people who do not follow this rule.
I disagree. The purpose of word problems like this is to exercise your problem solving skills. One important skill that you should have is determining whether you have enough information to get a reliable answer. Another is recognizing the assumptions that you make while analyzing a problem. Real life often gives you problems with out adequate information to solve them. It is good training to face similar situations where you have to admit ignorance or seek out more information before answering.
Sometimes in higher education, questions will be left vague because the instructor wants to see if you understand the concept well enough to recognize the missing variable/consideration. Or even that a listed variable is irrelevant.
If this problem were given as a short answer rather than multiple choice (which is also a reason to strongly consider the question was incomplete, since that's one of the few choices given), I would have probably written "assuming there are no taxes or fees on top of the listed price..."
I agree with you, Wanarunna. The two previous people who replied to you have never supervised a department of people and been held responsible for the work those people produce.
Once a supervisor's ass has been chewed out for his crew's bad work, he begins to be much more careful with how he words the assignments he gives to his subordinates. This problem would get a very serious rewording before it was assigned to a subordinate.
@@deezynar I have been a supervisor before. That's why I worded my response around education. This question would never be assigned to a subordinate because it doesn't make sense in a work setting to begin with...
@@isaac_marcus
Yes, the question as posed in the video is not clear enough to be used in most environments outside of mathematical education. We agree on that.
I tried to restate it to make it clearer, and I realized I couldn't come up with a better way of saying it. My inability bothers me more than the original question does, and that's not insignificant.
I suspect that many, if not all, of the people who answered $1.50 or $1 were using what Daniel Kahneman called "System 1" or "fast" thinking (in his book Thinking, Fast and Slow).
I understood it this way: The price is $1. But wait, there is more: a half of that price more. Therefore I thought it either should be $1.50 or it can't be solved because the price can't be $1 and $1.50 at the same time. After the solution was given, I added ":" after "costs" and then it made more sense to me: "A book costs: $1 plus half its price."
I thought the question was that it was adding price infinite amount of times
C = 1 + C/2
this makes no sense to me, if thats not wrong then in should be:
1 + 1/2, but then it makes no sense too because it says half its cost, meaning the infinity one could be true?
It's not issue of people failing at math but rather an issue of communication I thought it was ment to be read as "A book cost $1. Plus half its value. Hiw much is the book?" From there the book is a dollar half a dollar is $0.50 there for its $1.50. It's like a really bad riddle
there is no ambiguity given there is no "." or "," after the $1. I think it was made as a puzzle to confuse people when not in the context of mathematics.
@@sashime00 So if a book's cost is $1 plus a tax of 50%, how much is the book, and how can I not read that based on what's literally written out?
* meant
Yeah, I'm going to have to disagree with this one. I would have let it slide if the D choice wasn't available, but it was, meaning you should be interpreting the problem much more strictly, and in this case the meaning is ambiguous and that itself makes it not determinable. Appealing to the dictionary is a fallacy as it isn't the true authority, it is a attempt to codify language, but not infallible, hence why we have many dictionaries with different definitions. Appealing to the book also fails as they too can be wrong (you've had many incorrect solution given in this vary channel to other problems, so deferring to the answer key is not proper). I can definitely give that $2 is a potential solution, but not the ONLY solution, therefore it is not determinable.
Regarding the difference between "price" and "cost":
- For the *provider* of a product or service, "price" and "cost" should be different, with the former being bigger than the latter, because the difference between them is what we call "profit".
- For the *acquirer* of a product or service, "price" and "cost" are exactly the same thing.
hello from greece. a version of this question was in the math book we had in school when i was 7-8 years old. third grade if i remember correctly. our version was .. a brick weigh is 1 kilo and half a brick how much does the brick weigh? (sorry for my english)..
If this came from the Soviet Union, 'Price' and 'Cost' are definitely two different things. And it is definitely deliberately confusing.
I respectfully disagree, as a retailer, cost is totally different than price. Price is what you sell it for and cost is what it costs you, the seller. You should not have to jump to a conclusion that cost means price to get the answer. Poorly written question.
But the question never uses "cost" as a noun, only as a verb.
That doesn’t matter, if you look at it from the sellers point, it costs them x amount and is priced at y. The verbiage should have used one term, cost, or not had cannot be determined as an option for the answer.
@@Steve_Stowers That's reaching. The question is specifically worded in a tricky way, and the noun and the verb versions of "cost" have multiple meanings.
That's the fundamental problem with most of these "questions." They are a word trick rather than a math problem. And the solution relies on using the meaning the author wants you to use. To me, cost and price are two different things.
The price is the buyers cost.
I can not get to your answer from here at the book store. I'm trying to buy it for $2 and they say no. They say the price of the book is the sticker price. The cost to me at the cash register is half the price plus a dollar. They convinced me that is the answer: Half the price plus a dollar. You have to know the stocker price to produce a number.
Go argue with the book sellers. (Russians had no sticker prices. Price varied with your Party association.)
Had it in a few seconds. Then I noticed how long the video was. That, coupled with the title of the vid made me think I'd done something wrong. Spent 5 minutes trying to figure out if I'd missed something. Nope. 🤣🤣🤣
Buying this book is like falling into a math rabbit hole-$1 plus half its price, and then half of that, and half of that... it's the book that keeps on costing!
And if you keep on adding half till infinity you never get to the cash register!
sooo it costs a dollar plus 50 cents plus 25- hang on a minute, the book just costs 2 dollars again
@@adamrussell658 And yet, the cashier still takes your $2, hands you the receipt, and tells you to stop staring at the counter and let the person behind you make a purchase.
@@Moonlite_Kitsuneno. It costs
$1.50 in the first iteration
$1.50+$1.50/2 in the second
...
This already equals to $2.25
What I mean is that the price updates every time and the half of that gets added to the new price and so on.
This is a very common pattern found in (procedural) programming. So it's really not far fetched to think of the problem like this when you have a programming background.
I got the expected answer of $2, but I was expecting in the justification of the 4th answer some sort of explanation of why posted prices in USA often don't factor in tax. Also, I wonder how biased the polls were, since I suspect a large number of followers/subscribers of Presh are more mathematically literate than the general population. Interesting video either way, I enjoyed watching it and I can appreciate the effort it took to make this, and now I want to know where I can get a $2 book in 2024
Good tax jokes XD.
Also, yeah. Whats with the 39% percent of that answered wrong?Actually, algorithm probably, but still doesnt make much sense
This is the easiest one yet. Let T be the price of the book.
1 + T/2 = T
1 = T - T/2
1 = T/2
2 = T
The book is $2
Why does this video not address the price vs cost meaning, depending on context?
Due to the warding, you can not assume weather the cost is refereed from the customer's (who buys the book from the store) perspective or the seller's (who sells the book in their store).
To the customer, it costs the book's price.
To the store, it costs as much as they pay to the factory.
Since it is translated from Russian, in English it becomes unclear, but reading in Russian you would more or less be certain that is it x = 1 + (1/2)x
Is pretty clear in English too. The last part of the question refers to the cost, as does the first. There's no confusion. I think the only reason people pause is because they expect it's a trick question, while it's not.
But the book itself says the answer is $2, so it's not a translation issue.
Problem #37. That's is a fun coincidence.
Ah yes, the "random" number
6:21.
x = 1 + 0,5x
0,5x = 1
x = $2
What an interesting puzzle.
Are there rules against picking every answer? And then just showing how each answer meets the criteria for a correct answer.
Textbooks have been known to provide incorrect answers. You can't refer to the book as the correct answer, especially in another language. You can't expect someone to know a question comes from a Russian book in order to solve it. The words of the question are the question, nothing else. I still think cost and price are two very distinct things. They are different words for a reason. And here the question is clearly written as : c = 1 + p/2. You can't just assume c = p, because it's a common usage. Common usage is not a mathematical truth.
Mathematical truth is only the result of common usage, language itself is only the result of common usage. If enough people agree on a mathematical concept it becomes true, take Euclid's 5 postulates, we can't prove they are true yet we assume they are because we agree on it. So, by your logic we can't just assume a triangle is 180 just because it's common usage, another point is that mathematical truth changes over time, because the truth is we don't know everything about math. 2000 years ago negative numbers were not a thing, not they are, we even have to square root of negative numbers, which are in the most literal sense, imaginary. In conclusion, math is only a collection of commonly used methods for humans to express logical thinking, math and logic has historically been dictated by human opinions and there is no reason why our current math is true mathematical truth and not just another mistake future generations will look down at us for.
For a customer/ reader, the cost of the book is the price of the book. Overthinking basic stuff often leads to misery.
you are right. That is one of the logical fallacies, equivocation. no idea why all smart people in here get it wrong.
If this were explicitly presented in the context of “arithmetic problems” then it’d be unambiguous. It would also be unambiguous if it were phrased “the price of a book is $1 plus half its price, what is that price?” But when it’s presented as a “logic problem,” I don’t think you can simply assert “cost == price” in your solution, because the specific word choice in a logic problem is usually material to the solve.
plz edit “when it’s presented as…” to “if a reader is thinking about it as…” - I’m not saying “you presented it wrong!”
To some people, cost and price are two different concepts. Cost is how much money is spent to produce something. Price is what that something sells for. One could argue that this problem is unsolvable at best, and ambiguous at worst.
I think it would be interesting if the question was rephrased to change the word price to cost. Would this significantly alter the results you obtained, I wonder?
$2
I knew the problem in this variant: a brick weighs 1kg plus half a brick, when does a brick weigh?
Whenever you put it on a scale, that's when it weighs.
I think this worded far better than the book price question.
I also know this variant, it was popular in Italy, many years ago. In my math book there was a picture of a scale with a brick on one plate and half a brick and the weight of a kilo on the other plate. 😀
@@TheWerns not one bit better. Just people who dont have any common sense, nor they can understand such simple mistakes
I love this problem, because it's actually something I can understand. Somewhat (let's be honest). I answered that it was not determinable. However, I did ask CGPT the question as worded, and the answer is the same=$2. Then I asked AI this question:
What if I am selling three books. Book A, is priced at $2, book B, is priced at $3, and book C is priced at $10. My store sells all books for $1, plus 1/2 their price. What is the price of book C ?
CGPT: We know the original price of book C is $10. Thus,
𝑃=10
Therefore, the price of book C in the store is $6.
This is why I don't understand how you can say the book is $2. My logic can't get around this, and I'm pretty sure that my thinking is faulty. I'm using my best logic to determine how I must be wrong. But how am I wrong? How is AI doing the math as I think it could be computed, if I am wrong?
What a legend!
Love your style 🤗
Came for the math problem stayed for the social commentary
2 dollars
R.I.P. Alan 🙏
2$
I feel your answer depends on your understanding of the question
I think its 2 also, but many people think of "plus its cost" as a form of tax, and you don't add taxes onto the tax
One thing it does highlight is that having come to an answer, a lot of people don't work it backwards to check it's correct - which seems to me to be a very obvious thing to do.
Okay, so obviously the answer is supposed to be 2$ - but I have an explanation that would explain why one could vote for the "cannot be determined" answer: infinite recursion.
The formula b = 1 + b/2 implies that both "b" are the same. But one could argue that, to add half to the cost, one must first calculate the cost.
So, in this case you would expand it like this:
b = 1 + b/2
b = 1 + ( 1 + b/2) / 2
b = 1 + ( 1 + ( 1 + b/2 ) / 2) / 2
... and so on.
This is obviously unbounded and thus cannot be determined.
Okay, when thinking one step further, that is not "obviously unbounded", but just the geometric series.. yielding 2$...
@@originellerNickname You can literally simplify it by doing the equation in reverse then solve for be normally though
@@originellerNickname my favourite! "You used the wrong formula, but somehow got the correct answer" XD
COST AND PRICE. I haggled and bought a candle holder that was priced at 20, for 8. It's price was NOT it's cost.
Exactly !
I haven't taken algrbra in a while. Something confuses me. What happened to the b on the left side of the equation? If you subtract b/2 from both sides, wouldn't it be b - b/2 = 1 + b/2 - b/2? That would leave b - b/2 = 1. Where did b go after this?
subtracting half of b (b/2) from b leaves half of b. (b/2)
An example: half a cup plus half a cup equals 1 cup, so if you take away half a cup from 1 cup you're left with half a cup.
Is the problem understanding language or understanding math?
Perspective. From the bookseller's perspective, the cost is not the price. To the customer, the cost is same as the price.
Anyone who argues the answer is $2 is only looking at it from the customer's point of view.
The question is worded ambiguously, so the answer is not determinable.
To prevent confusions, the problem should be written like this: "The price of a book is $ 1 plus half its price. How much is it?"
That is no different
It felt really obvious that if you divide the price of the book in two baskets so to speak, and that one dollar is one half of the price,there needs to be a dollar in the other basket so you get two dollars.
This feels like very simple elementary school math.
So if the book is $1 plus 50% tax, how much is the book?
It's one of those questions that elementary schoolers are going to have an easier time with than adults, because they will just isolate the math and not the problem.
All the states I've lived in have had sales tax. If something is priced at $10, I know I'm really gonna pay closer to $11. To me, that means it costs around $11 to buy something priced at $10.
There's also fees, like brokerage fees when buying a house, or registration fees for a vehicle. You might also consider loans in a cost. My mortgage was around $200k (the list price of the house), but after a couple years and putting almost $30k in, i still owed about $190k. So if I had kept living there and kept the house until I'd paid it off, the price would have been vastly different from how much it actually cost.
We adults also use "cost" in far more metaphorical contexts than a child probably does. "This little maneuver's gonna cost us 51 years."
As I've grown older and more experienced, the less i associate the price with how much something costs in the end. I think the question just lacks some assurances of common variables, like "you're buying something in a store with no additional taxes or fees." (Granted this was apparently written in the Soviet Union and I don't know what the actual process of buying something there and then looked like)
It's a bit like how it would be a bit strange if a high school physics question asked "how long does it take this box sliding along the ground to come to a halt" but failed to tell you to ignore air resistance and gave you no information about the air density/pressure etc.
@@RevJRThat's a different question though. May I ask how it is relevant?
@@Runegrem Does the book cost $1 plus half its price?
Cost is the subject, and price is the object, the way the sentence is written, I think. The subject (cost) is relative to the object (price).
The point is, this isn't a math problem, this is a sentence diagram problem.
@@RevJR I'm not the best at grammar jargon, but the book is definitely the subject in the question. It's the thing performing the action of costing something. The price (the full price formula, not just the word) would be the object.
You turned a math question into a brain teaser question successfully
Let the cost of the book be 'x'
According to condition:
x=1+0.5x
0.5x=1
x=2
Therefore the book costs 2 dollars.
Half it's price not cost, therefore you cannot associate cost and price in the same variable.
@@axel3689 isn't cost and price the same thing?
It has to be 2 dollars