Question

ASB is selling boxes of candy as a fundraiser. ashley ordered one small box and 5 large box for a total of $38. Evan ordered two small boxes and three large boxes for a total of $34. What is the price for each type of box?

Answer 1

To determine what is the price for each type of box, we can create a system of linear equations:

Let x be the price for small boxes

Let y be the price for large boxes

1 small box and 5 large boxes for a total of $38.

`x+5y=38\text{ (1)}`

2 small boxes and three large boxes for a total of $34.

`2x+3y=34\text{ (2)}`

Substitute (1) in (2):

`2(38-5y)+3y=34`

Solve for y(price for large boxes):

`\begin{gathered} 76-10y+3y=34 \\ 76-34=7y \\ 42=7y \\ y=(42)/(7) \\ y=6 \end{gathered}`

Large boxes cost $6.

Therefore, small boxes:

`\begin{gathered} x+5(6)=38 \\ x=38-30 \\ x=8 \end{gathered}`

Small boxes costs $8.