Question

George and Riley are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. George sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Riley sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost of each of one small box or oranges and one large box of oranges.

Answer 1

The cost of small box of oranges is $7.

The cost of large box of oranges is $13.

Explanation:

It is given that,

3 small boxes of oranges and 14 large boxes of oranges for a total of $203.

11 small boxes of oranges and 11 large boxes of oranges for a total of $220.

Let us take,

• The cost of small box of oranges = x
• The cost of large box of oranges = y

The system of equations are framed as :

3x + 14y = 203 ---------(1)

11x + 11y = 220 ---------(2)

To solve these equations for x and y values :

Multiply equation (1) by 11 and equation (2) by 3

Subtract eq(2) from eq(1),

33x + 154y = 2233

- (33x + 33y = 660)

121 y = 1573

⇒ y = 1573 / 121

⇒ y = 13

∴ The cost of large box of oranges is $13.

Substitute y=13 in the eq(1),

⇒ 3x + 14(13) = 203

⇒ 3x + 182 = 203

⇒ 3x = 203 - 182

⇒ 3x = 21

⇒ x = 21 / 3

⇒ x = 7

∴ The cost of small box of oranges is $7.