Question

Mr. Sanchez’s class sold fruit pies for $1.32 each and Mr. Kelly’s class sold bottles of fruit juice for $1.77 each. Together, the classes sold 90 items and earned $140.40 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

a)
`k=48\\s=42`

b) Mr. Kelly’s class.

c) $29.52

Explanation:

a) Let's call:

s: the number of fruit pies sold by Mr. Sanchez’s class.

k: the number of fruit pies sold by Mr. Kelly’s class.

You can set up the following system of equations:

`\left \{ {{s+k=90} \atop {1.32s+1.77k=140.40}} \right.`

You can solve it by the Elimination method:

- Multiply the first equation by -1.32.

- Add both equations.

- Solve for k.

Then:

`\left \{ {{-1.32s-1.32k=-118.8} \atop {1.32s+1.77k=140.40}} \right.\\\\0.45k=21.6\\k=48`

Susbtitute k into any of the original equations and solve for s:

`s+k=90\\s+48=90\\s=42`

b) The amount of money earned by Mr. Kelly’s class was:

`48\ pies*\$1.77=\$84.96`

The amount of money earned by Mr. Sanchez’s class was:

`42\ pies*\$1.32=\$55.44`

Then, the class that earned more money was: Mr. Kelly’s class.

c) Subtract both amounts of money:

`\$84.96-\$55.44=\$29.52`