Math Problem Statement

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?

Solution

Let's define the variables:

  • Let ss be the cost of a small pizza.
  • Let mm be the cost of a medium pizza.
  • Let ll be the cost of a large pizza.

Based on the given information, we can set up the following equations from each package:

  1. Small Gathering Package: s+m+l=28s + m + l = 28

  2. Family Reunion Package: 4s+2m+l=584s + 2m + l = 58

  3. Huge Party Package: 6s+5m+4l=1356s + 5m + 4l = 135

We now have a system of three equations:

  1. s+m+l=28s + m + l = 28
  2. 4s+2m+l=584s + 2m + l = 58
  3. 6s+5m+4l=1356s + 5m + 4l = 135

Step 1: Eliminate ll

Let's subtract the first equation from the second to eliminate ll: (4s+2m+l)(s+m+l)=5828(4s + 2m + l) - (s + m + l) = 58 - 28 3s+m=303s + m = 30

This gives us a new equation: 3s+m=303s + m = 30

Step 2: Create another equation without ll

Next, we subtract the first equation from the third: (6s+5m+4l)(s+m+l)=13528(6s + 5m + 4l) - (s + m + l) = 135 - 28 [ 5s + 4m + 3l = 107

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations

Formulas

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

Theorems

Substitution and Elimination in Systems of Linear Equations

Suitable Grade Level

Grades 8-10