Andrew bought pizzas for his swim team. Pepperoni pizzas cost $13 and

SidR

Question mentions "he bought only pepperoni or combination pizzas."
Means only one category
And 184 is divided neither by 13 nor 17.so that's not possible

Could you please check question and confirm whether my understanding is correct or am I missing something

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The question isn't saying that either he bought ALL pepperoni or he bought ALL combination pizzas. It's saying that each pizza is one of either pepperoni or combination.

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

Hi All,

We're told that Andrew bought pizzas for his swim team; pepperoni pizzas cost $13 each, combination pizzas cost $17 each and he bought only pepperoni or combination pizzas (spending a total of $184 on pizzas). We're asked for the TOTAL number of pizzas he bought. This question can be solved in a number of different ways, but it has a great 'pattern-matching' shortcut that get you to the correct answer without too much math.

To start, it's worth noting that the combined cost of 1 pepperoni pizza and 1 combination pizza is $13 + $17 = $30. With a total of $184 of pizzas, (6)($30) = $180 is fairly close to that total. Notice that it's $4 less than what we need it to be... which is exactly the difference in price between a combination pizza and a pepperoni pizza.

So, if we buy 6 pepperoni pizzas and 6 combination pizzas, we'll spend $180 in total. If we 'swap' one pepperoni pizza for one combination pizza, then we'll end up spending 4 MORE dollars, for a total of $184. That would be 5 pepperoni pizzas and 7 combination pizzas --> a total of 12 pizzas.

Final Answer:

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Rich

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