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

Answer:

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

b)  Mr. Kelly’s class.

c) $29.52

Step-by-step 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:

$\ 84.96-\ 55.44=\ 29.52$