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# help

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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?

Mar 9, 2020

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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   Mar 9, 2020