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

Algebra ->  Matrices-and-determiminant -> 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      Log On


   

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) About Me  (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:
system%28x%2By%2Bz=600%2C12x%2B10y%2B8z=5900%2Cz=y%2B175%29


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

%28matrix%283%2C4%2C1%2C1%2C1%2C600%2C12%2C10%2C8%2C5900%2C0%2C-1%2C1%2C175%29%29


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 x=225, y=100, and z=275


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