Ben was in charge of ordering 16 pizzas for the office party. He ordered three types of pizza: Cheese, Pepperoni, and Supreme. The cheese pizzas cost $8 each, the pepperoni pizzas cost $10 each, and the supreme pizzas cost $12 each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If Ben spent a total of $156 on pizza, how many pizzas of each type did he buy?

Guest Mar 9, 2020

#1**+2 **

Ben was in charge of ordering 16 pizzas for the office party. He ordered three types of pizza: Cheese, Pepperoni, and Supreme. The cheese pizzas cost $8 each, the pepperoni pizzas cost $10 each, and the supreme pizzas cost $12 each. He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. If Ben spent a total of $156 on pizza, how many pizzas of each type did he buy?

Let x = the number of cheese pizzas, y the number of pepperoni and z be the number of supreme pizzas

And...."He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas. " ...translates as :

2 (8x) = 10y ⇒ 16x = 10y ⇒ x = (10/16)y = (5/8) y (1)

We have this system

x + y + z =16 (2)

8x + 10y + 12z =156 (3)

Sub (1) into (2) and (3) and we have that

(5/8)y + y + z = 16

8(5/8)y + 10y + 12z = 156 simplify these

(13/8)y + z = 16 ⇒ z = 16 - (13/8)y (4)

15y + 12z = 156 (5)

Sub (4) into (5)

15y + 12 [ 16 - (13/8)y] = 156

15y + 192 - (156/8)y = 156

15y - (156/8)y = 156 - 192

(120 - 156) /8 y = -36

-36 y = -36 (8)

y = 8 = the number of pepperoni pizzas

z = 16 - (13/8)(8)

z = 16 - 13

z = 3 = the number of supreme pizzas

x + 8 + 3 = 16

x + 11 = 16

x = 5 = number of cheese pizzas

CPhill Mar 9, 2020