Question

Tim and Kevin each sold candies and peanuts for a school fund-raiser. Tim sold 16 boxes of candies and 4 boxes of peanuts and earned $132. Kevin sold 6 boxes of peanuts and 20 boxes of candies and earned $190. Find the cost of each. Cost of a box of candy. Cost of a box of peanuts.

Answer 1

We have the following:

let x cost of a box of candy

let y cost of a box of peanuts

`\begin{gathered} \text{ Tim} \\ 16x+4y=132 \\ \text{ Kevin} \\ 20x+6y=190 \end{gathered}`

resolving the system of equations:

`\begin{gathered} 20x+6y=190 \\ 16x+4y=132\Rightarrow4y=132-16x\Rightarrow y=(132-16x)/(4) \\ \text{replacing:} \\ 20x+6\cdot((132-16x)/(4))=190 \\ 20x+198-24x=190 \\ -4x=190-198 \\ x=(-8)/(-4) \\ x=2 \end{gathered}`

now, for y

`\begin{gathered} y=(132\cdot16\cdot2)/(4) \\ y=25 \end{gathered}`

Therefore the cost of the box of candy is $ 2 and the cost of the box of peanuts is $ 25