# Solving the Given Augmented Matrices by ClassOf1

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Sub: Mathematics                                                                     Topic: Linear Algebra

Solving the Given Augmented Matrices

Question:
A group of students decides to sell pizzas to help raise money for their senior class trip. They sold
pepperoni for \$12, sausage for \$10, and cheese for \$8. At the end of their sales the class sold a total
of 600 pizzas and made \$5900. The students sold 175 more cheese pizzas than sausage pizzas. Set up
a system of three equations and three unknowns, use an augmented matrix to solve.

12 10      8 5900
1     1    1    600
0      1 1      175

Solve for the matrix.

Solution:

5     2 1475
1
6     3   3                   1
The augmented matrix gives 1                1     1 600          R1         R1
12
0      1 1       175

5      2 1475
1
6      3   3
1      1 325
To make a21      0, 0                            R2        R1    R2
6      3   3
0    1     1 175

1   0       1 50
1      1 325
To make a12      0, 0                            R1       5R2      R1
6      3  3
0    1     1 175

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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
Sub: Mathematics                                                                     Topic: Linear Algebra

1    0         1     50
To make a22 1 , 0          1       2     650        R2      6R2
0     1      1     175

1 0          1      50
To make a32       0, 0 1         2       650        R3     R2     R3
0 0         3       825

1 0 0 225
1
To make a13      0, 0 1 2 650                  R1          R3   R1
3
0 0 3 825

1 0 0 225
1
To make a33      1, 0 1 2 650                  R3          R3
3
0 0 1 275

1 0 0 225
To make a23      0, 0 1 0 100                  R2         2R3     R2
0 0 1 275

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