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Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming 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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luisejr77

Answer: One small box of oranges costs $7 and one large box of oranges costs $13.

Step-by-step explanation:

Let be "s" the cost in dollars of one small box of oranges and "l"  the cost in dollars of one small box of oranges.

Based on the data given in the exercise, you can set up the following System of equations:

[tex]\left \{ {{3s+14l=203} \atop {11s+11l=220}} \right.[/tex]

Use the Elimination Method to solve it:

- Multiply the first equation by 11 and the second one by -3.

- Add the equations.

- Solve for "l".

Then:

[tex]\left \{ {{33s+154l=2233} \atop {-33s-33l=-660}} \right.\\...............................\\\\121l=1573\\\\l=13[/tex]

- Substitute the value of "l" into any original equation and solve for "s":

[tex]3s+14(13)=203\\\\3s=203-182\\\\s=\frac{21}{3}\\\\s=7[/tex]