Question

Sandwich buns are sold in a package of either 8 or 12. How many ways can Matt buy exactly 48 buns?

Answer 1

6 packages of 8 buns

Answer 2

Matt can buy 48 buns in 3 ways:

... 6 packages of 8

... 3 packages of 8 and 2 packages of 12

... 4 packages of 12

_____

The least common multiple of 8 and 12 is 24. There are 2 ways to get 24 (3×8 or 2×12), and 2 groups of 24 in 48. Both groups can be of 8s or 12s or there can be one of each.