How much does a single book cost

Question

chria buys 8 books, but it turned out he was $7 short. what he did buy was 7 books and was left with $5 to spare. How much does a single book cost if all the books he was intrested in cost the same.

Answer 1

In this equation, X is the price of a book.  Chria has a set amount of money, and when he wanted to buy 8 books he found out that he had $7 too little.  We can represent the amount of money Chris has (we will call it Y) with this equation:  Y=8X-7

 

Chria was able to buy 7 books and have $5 left over.  So, we can also represent the amount of money that Chria has (still Y) with this equation:  Y=7X+5

 

He has the same amount of money either way.  The amount of money has not changed.  Since Y represents the original amount of money that Chria has in both equations, the other side of each equation should be equal to each other.

 

Y=8X-7

Y=7X+5

 

So,  8X - 7 = 7X +5.

 

You then solve for X.

Answer 2

x=cost of each book

8x-7 is how much money the person has ($7 short)

7x+5 is also how much money the person has ($5 to spare)

equate them

8x-7=7x+5

8x-7x=7+5

x=$12 per book

check: 8*12=$96 but $7 short means the person has $96-$7=$89

          7*12=$84 but $5 to spare means the person has $84+$5=$89