Question

8) Joe and Maria are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Joe sold 4 small boxes of tangerines and 12 large boxes of tangerines for a total of $124. Maria sold 11 small boxes of tangerines and 3 large boxes of tangerines for a total of $71. What is the cost each of one small box of tangerines and one large box of tangerines?

Answer 1

let

cost of each small box of tangerines = x

cost of each large box of tangerines = y

Joe sales

$4x+12y=124$

Maria sales

$11x+3y=71$

Therefore,

$\begin{gathered} x+3y=31 \\ x=31-3y \\ \text{Therefore,} \\ 11(31-3y)+3y=71 \\ 341-33y+3y=71 \\ 341-30y=71 \\ -30y=71-341 \\ y=\frac{-270}{-30} \\ y=9 \\ \\ x+3y=31 \\ x+3(9)=31 \\ x+27=31 \\ x=31-27 \\ x=4 \end{gathered}$

cost of one small box of tangerine = $4

cost of one large box of tangerine = $9