SOLUTION: Ben was in charge of ordering 32 pizzas for the office party. He ordered three types of pizza: Cheese, pepperoni and supreme. The cheese pizza cost $7 each, the pepperoni pizza cos

Question 1040893: Ben was in charge of ordering 32 pizzas for the office party. He ordered three types of pizza: Cheese, pepperoni and supreme. The cheese pizza cost $7 each, the pepperoni pizza cost $10 each, and the supreme pizza cost $13 each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If Ben spent a total of $314 on pizza, how many pizzas did he order?
Found 2 solutions by Fombitz, jorel555:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1. - Total number of pizzas
2. - Total cost of pizzas
.
.

3. - Relationship between cheese and pepperoni
From eq. 1,

Substituting from 3,

4.
From eq. 2,

5.
Multiply eq. 4 by 7 and eq. 5 by 4 and subtract them to eliminate C.

Then from 4,

and from 3,

Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
Let c=cheese pizza, p=pepperoni pizza, and s=supreme pizza. Then
c+p+s=32
7c+10p+13s=314
10p=2(7c);10p=14c
10c+10p+10s=320
7c+10p+13s=314
3c-3s=6;
7c+14c+13s=314
21c+13s=314
21c-21s=42
Subtracting the last equation from the second-to-last, we get
34s=272
s=8 supreme pizzas
p=14 pepperoni pizzas
c=10 cheese pizzas ☺☺☺☺

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