Question

A pizza store offers three different party packages of pizzas. The packages and prices are listed below. If pizzas cost the same individually or in a package, what is the cost of a large pizza? Small Gathering: 1 small, 1 medium, 1 large $28Family Reunion: 4 small, 2 medium, 1 large $58Huge Party: 6 small, 5 medium, 4 large $135

Answer 1

S+m+l=28
4s+2m+l=58
6s+5m+4l=135

Eliminate the variable l from the first 2 equations

s+m+l=28
-4s-2m-l=-58
-3s-m=-30

Elminiate the variable l from the last 2 equations

6s+5m+4l=135
-16s-8m-4l=-232
-10s-3m=-97

Now solve for s and m using the 2 equations without l

-3s-m=-30
-10s-3m=-97

9s+3m=90
-10s-3m=-97
-s=-7
s=7

Then plug in s into one of the equations without l

-3(7)-m=-30
-21-m=-30
-m=-9
m=9

Now plus in s and m into one of the original 3 equations

(7)+(9)+l=28
16+l=28
l=12

Final answer:
Small=$7
Medium=$9
Large=$12

I know it only asks for large but I wanted to show you how to find them all for future reference. :)

Answer 2

The Small=$7
Medium=$9
Large=$12