Question

For his troops' popcorn fundraiser sale, Mike sold caramel corn for $10, buttered microwave popcorn for $8, and lightly buttered popcorn for $7. By the end of the fundraiser, he had sold 400 items and made $3,272. If he sold twice as many lightly buttered microwave popcorn boxes as the buttered popcorn, how many boxes of each type of popcorn did he sell?

Answer 1

x = caramel corn
y = buttered
z = lightly buttered

x + y + z = 400
10x + 8y + 7z = 3272
2z + z + x = 400 <= here since he sold twice as many LB popcorn as buttered, I replaced the LB with 2z.

OK, since we have two of these equal to 400...

2z + z + x = x + y + z
3z = y + z
2z = y
Substitute this in for y.

x + 3z = 400 => 10x + 30y = 4000
10x + 16z + 7z = 3272 => 10z + 23z + 3272

Now subtract these two equations. 7z = 728, z = 104
2(104) = y
y = 208

104 + 208 + x = 400
x = 88

88 caramel popcorn, 208 lightly buttered and 104 buttered.