Tom and Jerry are selling fruit for a charity fundraiser

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

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x = cost of a small box of oranges
y = cost of a large box of oranges

3x + 14y = 203  {Tom sold 3 small boxes and 14 large boxes for $203}
11x + 11y = 220  {Jerry sold 11 small and 11 large for $220}

Multiply first equation by -11 and second equation by 3, to cancel the x's when added.

-33x - 154y = -2233  {multiplied first equation by -11}
33x + 33y = 660 {multiplied second equation by 3}
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-121y = -1573  {added the two equations together}
y = 13   {divided each side by -121}

Substitute 13, back in for y, into one of the two equations.

11x + 11y = 220  {second original equation}
11x + 11(13) = 220  {substituted 13, in for y, into second original equation}
11x + 143 = 220  {multiplied 11 by 13}
11x = 77   {subtracted 143 from each side}
x = 7  {divided each side by 11}

$7 for a small box and $13 for a large box

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