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Ben was in charge of ordering 32 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 $ 10 ​each, and the supreme pizzas 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 of each type did he​ buy?

Respuesta :

Answer:

cheese pizza = 10

Pepperoni pizza = 14

supreme pizza = 8

Step-by-step explanation:

Let the number of ordered pizza be

cheese pizza = c

Pepperoni pizza = p

supreme pizza = s

thus,

c + p + s = 32  ................(1)

Cost of cheese pizzas = $7

Cost of Pepperoni  pizzas = $10

Cost of supreme pizzas = $13

therefore,

7c + 10p + 13s = 314  ..................(2)

also,

He spent exactly twice as much on the pepperoni pizzas as he did on the cheese pizzas

10p = 2 × 7c

or

5p = 7c ..............(3)

or

p = [tex]\frac{\textup{7}}{\textup{5}}[/tex]

now,

multiplying equation (1) with 5, we get

5c + 5p + 5s = 160

now,

substituting value of 5c from equation (3)

5c + 7c + 5s = 160

or

12c + 5s = 160 ................(4)

and substituting the value of p in equation (2)

7c + 14c + 13s = 314

or

21c + 13s = 314        ..............(5)

solving  4 and 5

we get

  7 × ( 12c + 5s = 160 )

- 4 × ( 21c + 13s = 314 )

or

 84c + 35s = 1120

- 84c + 52s = 1256

----------------------------

-17s = -136

or

s = 8

substituting s in 5, we get

21c + 13 × 8 = 314

or

21c = 210

or

c = 10

substituting s and c in equation 1, we get

10 + p + 8 = 32

or

p = 14

therefore,

cheese pizza = 10

Pepperoni pizza = 14

supreme pizza = 8

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