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17 Jul 2025, 12:55
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Huey’s Hip Pizza sells two sizes of square pizzas: a small pizza that measures 10 inches on a side and costs $10, and a large pizza that measures 15 inches on a side and costs $20. If two friends go to Huey’s with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?
Updated on: 23 Jul 2025, 00:25
Originally posted by Sajjad1994 on 23 Jul 2025, 00:24.
Last edited by Sajjad1994 on 23 Jul 2025, 00:25, edited 3 times in total.
Last edited by Sajjad1994 on 23 Jul 2025, 00:25, edited 3 times in total.
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First, understand the story. It asks you to maximize how much pizza they can buy. The large pizza has a 50% greater side length in each direction, yielding a pizza that is 1.5 × 1.5=2.25 times the area, but the price “only” doubles—so they can get more pizza per dollar by buying more large pizzas.
Alone, they could each buy 1 small and 1 large pizza, for a total of 2 small and 2 large pizzas. But if they pool their money, they can buy a total of 3 large pizzas. The difference between the two scenarios is the difference in area between 1 large pizza and 2 small pizzas. The area of one large pizza is \(15^2 = 225\) square inches. The area of one small pizza is \(10^2= 100\) square inches, so the area of two small pizzas is 200 square inches. If they pool their money to buy an extra-large pizza rather than two small ones, they will get an additional 25 square inches of pizza.
25 square inches
First, understand the story. It asks you to maximize how much pizza they can buy. The large pizza has a 50% greater side length in each direction, yielding a pizza that is 1.5 × 1.5=2.25 times the area, but the price “only” doubles—so they can get more pizza per dollar by buying more large pizzas.
Alone, they could each buy 1 small and 1 large pizza, for a total of 2 small and 2 large pizzas. But if they pool their money, they can buy a total of 3 large pizzas. The difference between the two scenarios is the difference in area between 1 large pizza and 2 small pizzas. The area of one large pizza is \(15^2 = 225\) square inches. The area of one small pizza is \(10^2= 100\) square inches, so the area of two small pizzas is 200 square inches. If they pool their money to buy an extra-large pizza rather than two small ones, they will get an additional 25 square inches of pizza.
25 square inches
