Question

3. Mr. Sanchez’s class sold fruit pies for $1.65 each and Mr. Kelly’s class sold bottles of fruit juice for $1.36 each. Together, the classes sold 79 items and earned $118.17 for their school.
(a) Write and solve a system of equations that model the problem. Show all your work.
(b) Which class earned more money?
(c) How much more money did that class earn?

Answer 1

You solve with substitution

Answer 2

The linear equations, which class earned more and by how much is required.

The equations have been solved below.

Sanchez's class earned more money by $\ 3.93$

Let $x$ be the number of fruit pies sold.

$y$ be the number of bottles of fruit juice sold.

Total number of items sold = $118.17

$1.65x+1.36y=118.17$

$x+y=79$   $\times 1.65$

$1.65x+1.36y=118.17$

$1.65x+1.65y=130.35$

Subtracting the equations

$-0.29y=-12.18\\\Rightarrow y=\dfrac{12.18}{0.29}\\\Rightarrow y=42$

$1.65x+1.36\times 42=118.17\\\Rightarrow x=\dfrac{118.17-1.36\times 42}{1.65}\\\Rightarrow x=37$

Money earned by Sanchez class

$1.65x=1.65\times 37=\ 61.05$

Money earned by Kelly class

$1.36y=1.36\times 42=\ 57.12$

By how much

$61.05-57.12=\ 3.93$

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