Question

Ben was in charge of ordering 29 pizzas for the office party. He ordered three types of pizza: Cheese, Pepperoni, and Supreme. The cheese pizzas cost $7 each, the pepperoni pizzas cost $9 each, and the supreme pizzas cost $11 each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If Ben spent a total of $255 on pizza, how many pizzas of each type did he buy? Ben ordered cheese pizzas, pepperoni pizzas, and supreme pizzas

Answer 1

Set up the following

Let c stand for cheese, p for pepperoni and s for supreme

Cost of the pizzas. 7c + 9p + 11s = 255

Total pizzas. c + p + s = 29

Pepperoni to cheese cost. 9p = 2(7c)
p= (14/9)c

c+p+s=29
s=29-c-p

7c+9p+11s=255

Now substitute
7c+14c+11(29-c-p) = 255

21c+319-11c-11p=255
10c+319-11p=255
10c+319-11(14/9)c = 255
90/9c-154/9c= -64
-64/9c = -64
c = 9

Find p by substituting 9 for c in 9p=2(7c)

9p=2(7)(9)
9p=126
p=14

Substitute for c and p in c+p+s=29
9+14+s=29
23+s=29
s=6

Ben bought 9 cheese, 14 pepperoni and 6 sausage

Check:
7(9)+9(14)+11(6)=63+126+66=255