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.

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.

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.

Wait, this video is over 8 minutes long. Really curious how that question is going to get stretched.

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.

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.

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...

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.

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.

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.

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.

the true answer is that the statement is too ambigious and poorly worded

If you have to resort to a dictionary and parsing the language of the question, you're probably going about it wrong.

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.

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)

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

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.

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.

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.

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." :)

4:52 I have this book, but it cost more than $2.

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$.

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 (?

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

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.

It is absolutely confusing wording. Confusing word problems existed then and it exists now. The book it came from is called Moscow PUZZLES. Of course it's meant to be confusing. The problem is presented as a math problem, but it's actually a logic problem.

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.

I don't think the discourse around this question is due to an inability to perform simple math, but rather upon the writer's incompetent (or purposefully devisive) word choice. The validity of your answer is dependent upon your interpretation of what the $1 means. My first interpretation was that the book's price was changing from an initial cost of $1 to a value of one half higher. I consider this to be a completely valid interpretation because that is how prices in the real world work - discounts and upcharges are based on the book's initial price, not the actual price. This would cause the equation to actually be n = i + i/2 where n is the new price and i is the initial price of $1, resulting in a new price of $1.50.

$2, ez, you just lost a customer, and I saved 8 minutes of my time

It’s ridiculous to set a question that relies on duplicate interpretations of the words in the question. I would expect that an examiner would seek to ensure there was no ambiguity in a question rather than try to set a trap like this 👎

How on Earth are people having problems with "An object costs X plus half it's price. What is its price?"

There's probably a large capture of "just show me the answer" people in the "can't be determined" option.

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.

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.

Your explanation of 'price' can't explain a half price sale. Quite often the cost of an item is not its price. Perhaps if you buy a 1$ chocolate bar there is a voucher inside for a book at half its price.

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.

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.

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.

I can see where you're coming from with the idea that the terms "price" and "cost" can be used interchangeably but that's just a matter of your being a math and economics guy rather than an english guy. "Price" and "cost," even in the context of being viewed from an entirely consumer perspective, do not have precisely the same meaning. The price of a thing is the value placed on its sticker on the shelf. How much it costs is the price plus any miscelaneous taxes or fees on the purchase. Outside the US, most purchases will have those as the same value but within the US and with quite a number of intangible products they simply aren't. 2 may be the intended answer and one that's easy to come to but it's an answer that relies on taking the written portion of the process much less precisely than the mathematics. Price being a subset of cost, the answer is indeterminate without the price being given or at least information that can lead to it being given. Given that the question is not originally in english though, we can mark that down as a translation error; someone trying to avoid redundance in the writing without considering the mathematical implications of changing the word used that way.

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!

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! 😅

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

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.

If A=B+A and B=A+C, then which variables can have their values determined, if any.

I'm curious to know whether the Russian version uses the same word for price/cost or not!

I like how you dont disprove the reasoning for getting the wrong answer. Its mainly just a misinterpretation of the problem, but nonetheless, in an 8 minute long video it should be discussed. If we assume the price is originally $1, and then the price is increased by 50%, the new price is $1.50. If you then think that it is continuously increased by 50%, the price would increase indefinitely. By saying the "book costs $1" the question confuses the reader. Whether it is intended or not is irrelevant.

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.

My answer is 2. Still: you could have checked the russian original to determine the intended meaning of the question. The supposed ambiguity probably does not exist there and can be discarded as an error of translation for those arguing for that.

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.

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%.

0:14 easy, E (it is a value that approaches infinity over time)

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.

People arguing that it can't be determined because of the "cost vs price" problem are intellectually lazy - they refuse to engage with the problem by hiding behind unreasonable semantic issues

$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.

I thought it was $1.50 because the book cost is $1 + half its price (0.50), but see I'm wrong.

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.

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."

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.

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.

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.

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

Ok, I get it...... I don't like it, but I get it.............. I originally read it as: A book costs a $1.00 (plus 1/2 its price). Apparently it is saying: A book costs ($1.00 plus 1/2 its price). So the $2.00 book is ($1.00 plus half its price ($1.00)).

Taking the statement as originally worded, the correct equation is, as you say, b = 1 + b/2. b = 1 + b/2 => b - b/2 = 1 => 2b/2 - b/2 = 1 => (2b - b)/2 = 1 => b/2 = 1 => b = 2 Apart from the reason given, where 'cost' is interpreted to mean 'cost of production', the only other way I can think of to reach the conclusion that the cost cannot be determined is to assume that the statement is incomplete, and expand it to read "A book NOW costs $1 plus half its ORIGINAL price", which would make the current cost impossible to determine.

On first though I was duh easy 1,5$. But when you wrote down the formula: b=1+b/2 it all made sense and ofc its 2$.

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.

6:21. x = 1 + 0,5x 0,5x = 1 x = $2 What an interesting puzzle.

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 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

If this came from the Soviet Union, 'Price' and 'Cost' are definitely two different things. And it is definitely deliberately confusing.

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.

In business, cost and price are not synonymous with each other. This 'problem' illustrates why people in business should never use academics in their businesses: too many problems resulting.

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?

Denial: $1.50 Anger: it can’t be solved Bargaining: let’s just test it to make sure Depression: tempted to just click on the video to find out Acceptance: $2

Bro had to become matpat just to discover 1$ plus half of it (0.5) Is 1.5$

But to a consumer cost = price. The question would have been clear had "cost" been replaced with "cost to produce". Or if you had said, it had been marked up by 50%. The audience is the 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

How are you associating price and cost as the same thing when it isnt even given in the question, the value cannot be determined is the right answer.

Mathematics is about rigour and unambiguity. Therefore, if it’s a mathematics problem, we should not accept that price and cost can be used interchangeably. Going from having 28% to 22% on the right answer is an evolution, but in the wrong way. You should be rooting for rigour and unambiguity, not for the perpetuation of ambiguous wording of problems. This is not an English test, it’s a maths test.

Been watching this channel for years and i think we’ve reached a new low. Can we do some real math, please?

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.

I presume a lot of Americans are defaulting to adding sales tax to get $1.50. 50% sales tax is an unrealistic level, but is a common process. I looked at the problem and did the sum of infinite inverse powers of two to accidentally get the correct answer.

If a book costs $2 to make and it sold for the same amount it cost to produce, what was its price? A) $2 B) cost and price can not be the same C) Hey, you didn't include sales tax D) Obviously misleading due to inflation

Hope you have a good day, to those reading this

This didn't solve anything, the question is ambiguous and more a problem of semantics. If cost is defined as the same value as price then the answer must be 1.5.

At some point you should remake this, but word it like this: A book costs $1 plus half its cost. How much does it cost?

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?

this type of problem where it is the semantics of terms used in the definition of the question is something I fought hard to remove as a 45 year veteran of teaching Y12 maths methods. Students should be tested on their ability to successfully recall theories and be able to apply or modify their approach to solve given the problem and NOT be a function of the decoding of the awkward use of the language.

It does NOT say One half of a book costs $1.. it says it cost $1, and then adding half its price which is .50 cents. It is like saying what is $1 plus half again. If you want it to equate to $2 then reword the question.

The Moscow Puzzles! I knew I've seen this puzzle before. I still own it. Lovely book, an absolute classic. Highly recommended. 😊

The length of a stick is 1 yard plus half its length. How long is the stick? 1 yard? 1.5 yards? 2 yards? Not enough info? Come on people, only 61% solved this?!

This is a very bad question in how misleading it is. One could argue that the interpretation of the riddle (because that is where this belongs) is that the books price is being stated as $1. Nobody in your life will speak so cryptically, so it is easy to take this at face value as the price being a dollar plus half the cost. This is more gotcha riddle than genuine qiestion.

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?"

Sorry, I don't see a problem here. As others have said, it's obviously $2.

the problem is that if you are approaching this from a mindset of mathematical variables, you don't just assume different terms are interchangeable, why use cost and price in the same question if they mean the same thing? It is an entirely fair assumption that they are in some manner different. This is very similar to using pounds and grams in the same question and assuming that people will just measure pounds as on earth at sea level. Provided the person is fluent in imperial and metric of course. This is a trick question, it is an intentional wording and anyone looking at it briefly and assigning cost and price as different variables will quickly answer "nice try, that's a trick question that can't be answered because the right answer of "it can't be determined" will be reported as the wrong answer because someone pulls out a dictionary and starts going on about synonyms. It is a no win question translated to run on assumptions that we can no longer make with social media questions that are all about the "gotcha, I'm smarter than you".

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.

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.

Why not asking directly: b = b/2 + 1 lets see how many would give the right answer. Not a math problem.

Ignoring the whole argument of price and cost not being the same thing, from how you stated it, I immediately jumped to the conclusion of $1.50. Why? The definition of the word “it/its” is “used to refer to a thing previously mentioned or easily identified.” according to Google (I cannot state a source, as google did not supply one, though I checked the Merriam Webster definition and it is very similar). In this case, the thing previously mentioned was “a book costs 1 dollar” and then, when the sentence stated “plus half ITS price” I was led to the conclusion that the book costs $1.50. I’m not going to be like some people now and tell you about how you suck or anything, because I’m not writing this because I think I’m better than everybody, I just have too much time on my hands lol- have a good day

Retailers make 100% mark up. That 100% mark up is half the cost. If it cost 100% + 100% then it costs 200%.