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.
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}  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 Ask the House
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