Question

1. matt and mary are selling fruit for a school fundraiser. customers can buy small boxes of oranges and large boxes of oranges. matt sold 3 small boxes of oranges and 4 large boxes of oranges for a total of $73. mary sold 10 small boxes of oranges and 10 large boxes of oranges for a total of $200. find the cost of one small box of oranges and one large box of oranges.

Explanation:

Step1: Define variables

Let $x$ = cost of 1 small box, $y$ = cost of 1 large box.

Step2: Set up equations

From Matt's sales: $3x + 4y = 73$
From Mary's sales: $10x + 10y = 200$ (simplify to $x + y = 20$)

Step3: Solve simplified equation for $x$

$x = 20 - y$

Step4: Substitute into first equation

$3(20 - y) + 4y = 73$
$60 - 3y + 4y = 73$
$60 + y = 73$

Step5: Solve for $y$

$y = 73 - 60 = 13$

Step6: Solve for $x$

$x = 20 - 13 = 7$

Answer:

The cost of one small box of oranges is $\$7$, and the cost of one large box of oranges is $\$13$.