SOLUTION: I am lost with this assignment, HELP! I do not understand hwo these are answered! 4. A group of students decides to sell pizzas to help raise money for their senior class trip.

Question 151324: I am lost with this assignment, HELP! I do not understand hwo these are answered!
4. 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, and show all work to receive full credit.
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.

D. Solve for the matrix. Show all work to receive full credit.

E. How many of each type of pizza were sold?

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(48568) (Show Source):
You can put this solution on YOUR website!
4. 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, and show all work to receive full credit.
-----------------------------------
A. What are the three unknowns?
p = # of pepperoni
s = # of sausage
c = # of cheese
-----------------------------------
B. Write a separate equation representing each of the first three sentences.
Quantity Eq: p + s + c = 600
Value Equat: 12p + 10s + 8c = 5900
Quantity Eq: 0p - s + c = 175
---------------------------------------
C. Determine the augmented matrix that represents the three equations.
---------------------------------------
D. Solve for the matrix. Show all work to receive full credit.
Use any method to get:
p = 225
s = 100
c = 275
-------------------

E. How many of each type of pizza were sold?
See answers to "D".
======================
Cheers,
Stan H.

Answer by jim_thompson5910(21685) (Show Source):
You can put this solution on YOUR website!
a)
Let x=# of pepperoni sold, y=# of sausage sold, and z=# of cheese sold

b)
Since there are 3 unknowns, we need 3 equations:

Equation #1:
First, since they sold "pepperoni for $12, sausage for $10, and cheese for $8" and collected $5,900, this means that

Equation #2:
Also, we know that the students sold 600 pizzas total. So this means that the sum of all of the pizzas sold was 600. So this translates to .

Equation #3:
Finally, since they sold "175 more cheese pizzas than sausage pizzas", this makes the equation

Getting all of the variables to one side for equation 3 gives us:

So we have the system

c)

This means that we have the augmented matrix matrix

d)

Solution was generated by the Linear Algebra Toolkit

=============================================================

Answer:

So the solutions are , , and (these values form the right hand column of the augmented matrix).

So this means that they sold 225 pepperoni pizzas, 100 sausage pizzas, and 275 cheese pizzas.