Question

Lea and Rob are selling fruit for a school fundraiser. Customers can buy small boxes of orangesand large boxes of oranges. Lea sold 2 small boxes of oranges and 1 large box of oranges for atotal of $12. Rob sold 3 small boxes of oranges and 1 large box of oranges for a total of $16.Find the cost each of one small box of oranges and one large box of oranges.

Answer 1

The first step is to define the system of equations.

Take x and y as the cost of a small box and a large box respectively.

`\begin{gathered} 2x+y=12 \\ 3x+y=16 \end{gathered}`

Solve the system.

`\begin{gathered} 2x+y=12 \\ y=12-2x \\ 3x+y=16 \\ y=16-3x \end{gathered}`
`\begin{gathered} 12-2x=16-3x \\ 3x-2x=16-12 \\ x=4 \end{gathered}`
`\begin{gathered} y=12-2x \\ y=12-2\cdot4 \\ y=12-8 \\ y=4 \end{gathered}`

A small box costs $4 and a large box costs $4 too.