Question

Using the equation from question 1 (also shown below), find another combination of popcorn and drinks that she can purchase for $45.

5x + 3y = 45

Answer 1

We want integer, nonnegative solutions of 5x + 3y = 45.

Modulo 3 gives 2x ≡ 0 (mod 3), so x ≡ 0 (mod 3). Let x = 3t. Then
15t + 3y = 45 ⇒ y = 15 − 5t.

For t = 0,1,2,3 we get the nonnegative solutions:
- t=0: x=0, y=15
- t=1: x=3, y=10
- t=2: x=6, y=5
- t=3: x=9, y=0

So another valid combination is 6 popcorn and 5 drinks (5·6 + 3·5 = 30 + 15 = 45).