SOLUTION: A group of students decides to sell pizzas to help raise money. They sold pepperoni for $12, sausage for $10, and cheese for $8. The class sold a total of 600 pizzas and made $59

Question 190631: A group of students decides to sell pizzas to help raise money. They sold pepperoni for $12, sausage for $10, and cheese for $8. The class sold a total of 600 pizzas and made $5900. The students sold 175 more cheese pizzas than sausage. Set up a system of three equations and three unkowns, use the augemented matrix to solve.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let
x = # of pepperoni pizzas sold
y = # of sausage pizzas sold
z = # of cheese pizzas sold

First, translate the sentences to get the following system:

Next, transfer the coefficients and the constants to form the augmented matrix:

Now let's perform the row reduction to solve for x, y, and z (rref steps provided by The Linear Algebra Toolkit):

Since the last column has the values 225, 100, and 275, this means that , , and

So the students sold 225 pepperoni pizzas, 100 sausage pizzas, and 275 cheese pizzas.

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