Math Question I need help with quick

Question

Paperback books cost $5 each and hardcover books cost $7 each. I spend exactly $86 on

books of these two types. What is the maximum number of books that I would have

bought?

Answer 1

5p + 7h = 86

86/5 = 17 1/5

5x16 = 80 + 6

5x15 = 75 +11

5x14 =70 +16

5x13 =65 +21****

max possible total books are 13 paperback and 3 hardback

costing 5(13) +3(7)

= $65 +$21 = exactly $86

13+3 = 16 is the max possible number of books if you spend exactly $86