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.
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