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?
+128473 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
