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Can anyone tell me exactly what is the question that is being asked in English for this equation? I am confused.

Please check the link for the video: https://youtube.com/shorts/mGDnsbKr7IM?si=3eLrjOzLffTp3SBb

A book costs \$1 plus half its price. How much does it cost?

A. \$1

B. \$1.50

C. \$2

Is the answer not \$1.50?

The answer for this problem is \$2.

Is he actually asking how much more of a price will it cost if you add another $1 plus half its price on top of the current book’s price?

Meaning let’s say the book cost \$2 and by adding another \$1 plus half its price, it will be another \$2 (hence the answer \$2) which makes the total \$4.

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MeGrammar
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    $x =1 + \frac{x}{2}$ where $x$ is the cost in dollars. – Sahaj Feb 19 '24 at 12:23
  • Where do you get the answer of 1 <- to plus it with x/2 – MeGrammar Feb 19 '24 at 12:26
  • I would not be too worried, it was always my feeling that this kind of problem is not as much about math as about weird games played with the natural language. It is just a convoluted way of saying "1 dollar is $1-\frac12$ of the price of the book, how much is the book". – Michal Adamaszek Feb 19 '24 at 12:44
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    To understand why answer C is correct, I suggest that you just try to verify that it works. Suppose the price of the book is $2. Then what's half its price, would you say? – Hans Lundmark Feb 19 '24 at 12:56
  • Your $$2$ vs. $$4$ example at the end of your question is adding the price of the book to half of the price of the book. But that doesn't happen anywhere in the problem statement. –  Feb 19 '24 at 13:17
  • Then the question should be “A book costs half of its price plus $1” or “A book costs X which is plus $1 and half of its price” else it makes no sense for it to be $2. – MeGrammar Feb 19 '24 at 13:45
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    What difference would that make? Addition is commutative, so “1 dollar plus half its price” is the same thing as “half its price plus 1 dollar”. (Except that the first formulation is slightly better, since it precludes the possible misinterpretation “half (its price plus 1 dollar)”.) – Hans Lundmark Feb 19 '24 at 14:15
  • I know “$1 dollar plus half its price” is the same as “half its price plus $1” now but however the inversion makes the interpretation much easier as I am confused having thought that the cost of the book is $1 and now i need to add half of the $1. With the inversion, I immediately able to understand that I need to find the book’s price before I can know “half of its price” then I need to add $1 (which an addition but not the book’s price). Of course after understanding the inversion meaning, once it is inverted back to the original it becomes the same (obvious as the inversion) – MeGrammar Feb 19 '24 at 16:03
  • But I understand now, thanks for everyone’s help. Appreciate it. No longer confused. – MeGrammar Feb 19 '24 at 16:09

1 Answers1

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This is a very famous problem.

The solution is as follows:

Let the price of the book be $x$. Then according to the question we have $$1+\frac{x}{2}=x$$ $$\implies 1=\frac{x}2$$ $$\implies\boxed{\color{red}{x=2}}$$

The question asks you the price of one book. It says that the book costs $1$ dollar, plus half it's price. Emphasis on the comma pls.

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