Question

Four friends go out to lunch together. Mike orders a personal pizza with 2 toppings for $7.00. Dustin orders a personal pizza with 5 toppings for $9.25. Lucas orders a calzone with 1 topping for $5.75. Will orders a calzone with 4 toppings for $8.75. For what number of toppings is the price of a personal pizza the same as a calzone?

Answer 1

To determine when the price of a personal pizza equals that of a calzone, we set up linear equations based on given prices and toppings, and solve for 'x,' the number of toppings. The intersection point of both equations provides the number of toppings for which the price of a pizza is equal to that of a calzone.

Step-by-step explanation:

To find out when the price of a personal pizza with a certain number of toppings is the same as a calzone with the same number of toppings, we can create two linear equations based on the provided information and find the point where they intersect.

Let x be the number of toppings, and P_pizza(x) and P_calzone(x) be the price functions for a personal pizza and a calzone respectively.

Using Mike and Dustin's orders, we can set up the equation for a personal pizza as follows:
P_pizza(x) = 7 + (9.25 - 7) / (5 - 2) * (x - 2) = 7 + 2.25 / 3 * (x - 2)

Using Lucas and Will's orders, we can set up the equation for a calzone as follows:
P_calzone(x) = 5.75 + (8.75 - 5.75) / (4 - 1) * (x - 1) = 5.75 + 3 / 3 * (x - 1)

To find the number of toppings for which P_pizza(x) = P_calzone(x), we need to solve the following equation:
7 + 0.75 * (x - 2) = 5.75 + 1 * (x - 1)