Question

Nine books are to be bought by a student. Some cost $6.00 each and the remainder cost $6.50 each. If the total amount spent was $56, how many of each book are bought?

Answer 1

Buy n books at $6. The total cost is

6n + 6.5(9-n) = 56
6n + 58.5 - 6.5n
.5n = 2.5
n = 5

5 at $6 + 4 at $6.50 = 30 + 26 = $56

Answer 2

You can also do that in your head as follows:

Books cost $6 and $6.50, the difference is $0.50.

9 books at $6 each cost $54.

You then have $2 left, good for exchanging for 4 books at $6.50. So a 4 at $6.50 and (9-4)=5 at $6.00.