SidR wrote:
Andrew bought pizzas for his swim team. Pepperoni pizzas cost $13 and combination pizzas cost $17 and he bought only pepperoni or combination pizzas. He spent a total of $184 on pizzas. How many pizzas did he buy?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Letting p = the number of pepperoni pizzas bought and c = the number of combination pizzas bought, wee can create the equation:
13p + 17c = 184
13p = 184 - 17c
p = (184 - 17c)/13
We can see we can buy at most 10 combination pizzas. (If the value of c were more than 10, then the number of pepperoni pizzas bought would be negative.)
If c = 10, then p = (184 - 170)/13 = 14/13, which is not an integer.
If c = 9, then p = (184 - 153)/13 = 31/13, which is not an integer.
If c = 8, then p = (184 - 136)/13 = 48/13, which is not an integer.
If c = 7, then p = (184 - 119)/13 = 65/13 = 5, which is an integer.
Therefore, a total of 7 + 5 = 12 pizzas are bought.
Answer: A
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