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Writing the Given Word Problem in the Form of Augmented Matrices

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"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. a. What are the three unknowns? b. Write a separate equation representing each of the first three sentences. c. Determine the augmented matrix that represents the three equations. "

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									       Mathematics
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Sub: Mathematics                                                                   Topic: Linear Algebra

Writing the Given Word Problem in the Form of 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.

   a. What are the three unknowns?

   b. Write a separate equation representing each of the first three sentences.

   c. Determine the augmented matrix that represents the three equations.

Solution:
   a. x - The number of pepperoni pizzas

        y - The number of sausage pizzas

        z - The number of cheese pizzas

   b. Since they sold pepperoni for $12, sausage for $10, cheese for $8 and made $5900, we get the
        first equation as 12 x 10 y 8 z           5900 .

        Since they sold a total of 600 pizzas, we have the second equation as x                       y   z   600

        Since they sold 175 more cheese pizzas than sausage pizzas, we have y 175                                   z , that is
        z    y 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
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Sub: Mathematics                                                                   Topic: Linear Algebra

                                                                              12 10        8 5900
   c. The augmented matrix representing the equations is 1                           1     1    600
                                                                               0      1 1       175




                                www.classof1.com/homework-help/math
 *The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
                              submitting the same in lieu of their academic submissions for grades.
Sub: Mathematics                                                                    Topic: Linear Algebra

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