Question

Kristin and Kathryn are selling fruit for a school fundraiser. Customers can buy small boxes of grapefruit and large boxes of grapefruit. Kristin sold 2 small boxes of grapefruit and 6 large boxes of grapefruit for a total of $132. Kathryn sold 10 small boxes of grapefruit and 11 large boxes of grapefruit for a total of $299. What is the cost of one small box of grapefruit and one large box of grapefruit?

A) Small box of grapefruit: $9, Large box of grapefruit: $19.
B) Small box of grapefruit: $19, Large box of grapefruit: $9.
C) Small box of grapefruit: $12, Large box of grapefruit: $22.
D) Small box of grapefruit: $14, Large box of grapefruit: $12.

Answer 1

By setting up a system of linear equations based on the sales of Kristin and Kathryn, we find that one small box of grapefruit costs $9 and one large box costs $19 (option A).

Step-by-step explanation:

To solve the problem of finding the cost of one small box of grapefruit and one large box of grapefruit based on Kristin and Kathryn's sales, we can set up a system of linear equations. Let's denote the cost of a small box as s, and the cost of a large box as l.

Kristin's sales: 2s + 6l = $132 (1)

Kathryn's sales: 10s + 11l = $299 (2)

Multiplying equation (1) by 5 gives us 10s + 30l = $660. By subtracting equation (2) from this, we eliminate s and can solve for l:
19l = $361
l = $19 (after dividing both sides by 19)

Substitute l = $19 into equation (1):
2s + 6(19) = $132
2s + $114 = $132
2s = $18 (after subtracting $114 from both sides)
s = $9 (after dividing by 2)

Therefore, the cost of one small box of grapefruit is $9, and one large box of grapefruit is $19.