Find the cost each of one small box of tangerines and one large box of tangerines.

Question

Beth and Jessica are selling fruit for a school fundraiser. Customers can buy small boxes of

tangerines and large boxes of tangerines. Beth sold 8 small boxes of tangerines and 1 large box

of tangerines for a total of $99. Jessica sold 3 small boxes of tangerines and 2 large boxes of

tangerines for a total of $68.

Answer 1

Let x = small box

Let y = large box

8x + y = 99.. equation 1

3x + 2y = 68.. equation 2

Re-Arrange equation 1 by subtracting 8x on both sides

8x - 8x + y = 99 - 8x

y = 99 - 8x... new equation 1

substitute new equation 1 into equation 2

3x + 2(99 - 8x) = 68 .... expand/distribute

3x + 198 - 16 x = 68 ... simplify/combine like terms

-13x + 198 = 68 .... Subtract 198 on both sides

-13x + 198 - 198 = 68 - 198

-13x = -130... Divide by -13 on both sides

x = 10

Substitute x = 10 into new equation 1 (y = 99 - 8x)

y = 99 - 8(10)

y = 99 - 80

y = 19

Therefore, the price of small boxes = $10, and the price of the large boxes = $19