Chapter A.8, Problem 24AYU

To determine

To find: A candy store sells boxes of candy containing caramels and cremes. Each box sells for $\$12.50$ and holds 30 pieces of candy (all pieces are the same size). If the caramels cost $\$0.25$ to produce and the cremes cost $\$0.45$ to produce. How many of each should be in a box to yield a profit of $\$3$?

Answer to Problem 24AYU

10 cremes in each box.

Explanation of Solution

Let $C=$ number of caramels and $M=$ number of cremes.

Total candy equation: $C+M=30$.

That is $C=\left(30-M\right)$.

Therefore,

$0.25C+0.45M=12.50-3.00$

$0.25C+0.45M=9.50$

$0.25\left(30-M\right)+0.45M=9.50$

$-0.25M+0.45M=9.50-7.50$

$0.20M=2.00$

Therefore, $M=10$ cremes in each box.