Answered

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A group of 15 people each bought both a book that cost x dollars and a bookmark that cost $1. A group of 3 people each bought both a book that cost x dollars and a backpack that cost $36. Both groups spent the same amount of money. What is the price of the book?

Sagot :

absimmons20231

Answer:

$1.40

Step-by-step explanation:

LanceLongFei

Answer:

The price of the book is $7.75.

Step-by-step explanation:

Let's first establish an equation.

If I buy a book costing [tex]x[/tex] dollars and a bookmark costing 1 dollars, I will have spent [tex]x + 1[/tex] dollars. So a group of 15 people doing the same will have spent [tex]15(x+1) = 15x + 15[/tex] dollars.

Analogously, the group of 3 people has spent [tex]3(x+36) = 3x + 108[/tex] dollars.

Since we know that both groups spent the same amount of money, we can set the two expressions equal to each other:

[tex]15x+15=3x+108\\12x=93\\x=7.75[/tex]

Because [tex]x[/tex] was the price of the book, which was asked for in the question, we conclude that the answer is $7.75.

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