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mel-nik [20]
2 years ago
5

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.
Mathematics
1 answer:
worty [1.4K]2 years ago
7 0

The cost of small box of oranges is $7.

The cost of large box of oranges is $13.

<u>Step-by-step explanation:</u>

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

<u>The system of equations are framed as :</u>

3x + 14y = 203  ---------(1)

11x + 11y = 220  ---------(2)

<u>To solve these equations for x and y values :</u>

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

Subtract eq(2) from eq(1),

 33x + 154y = 2233

- <u>(33x + 33y = 660)  </u>

  <u>        121 y = 1573  </u>

⇒ 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.

<u />

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