Question

A holiday shop packages fruitcake slices in packs of 2, muffins in packs of 4, and mini pies in packs of 16.
What is the least number of each pack needed so the total number of desserts is the same?

Answer 1

Let a,b,c be the numbers of packs of fruitcake (2), muffins (4), and mini pies (16). We need
2a = 4b = 16c.
From 2a = 4b, a = 2b. From 4b = 16c, b = 4c. So a = 8c. The smallest positive c is 1, giving
a = 8, b = 4, c = 1,
for 16 desserts of each kind.