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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (Show Source):
You can put this solution on YOUR website!
1.C%2BP%2BS=32 - Total number of pizzas
2.7C%2B10P%2B13S=314 - Total cost of pizzas
.
.
10P=2%287C%29
10P=14C
3.5P=7C - Relationship between cheese and pepperoni
From eq. 1,
5C%2B5P%2B5S=160
Substituting from 3,
5C%2B7C%2B5S=160
4.12C%2B5S=160
From eq. 2,
7C%2B14C%2B13S=314
5.21C%2B13S=314
Multiply eq. 4 by 7 and eq. 5 by 4 and subtract them to eliminate C.
84C%2B35S-84C-52S=1120-1256
-17S=-136
S=8
Then from 4,
12C%2B5%288%29=160
12C=120
C=10
and from 3,
5P=7%2810%29
P=14

Answer by jorel555(1290) About Me  (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 ☺☺☺☺