A large cheese pizza at Peter’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Gavin’s Pizzeria is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Peter’s Pizzeria and Gavin’s Pizzeria in order for the pizzas to cost the same, not including tax?

Question

A large cheese pizza at Peter’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Gavin’s Pizzeria is $7.30 plus $0.65 for each topping. How many toppings need to be added to a large cheese pizza from Peter’s Pizzeria and Gavin’s Pizzeria in order for the pizzas to cost the same, not including tax?
Responses
A	33
B	44
C	55
D	2

GPT-4o mini · Answer

Let $ x $ represent the number of toppings added to the pizza. The cost of a large cheese pizza at Peter's Pizzeria can be expressed as: $$ C_P = 6.80 + 0.90x $$ The cost of a large cheese pizza at Gavin's Pizzeria can be expressed as: $$ C_G = 7.30 + 0.65x $$ To find the number of toppings needed for the pizzas to cost the same, we set the two cost equations equal to each other: $$ 6.80 + 0.90x = 7.30 + 0.65x $$ Now, we will isolate $ x $. 1. Subtract $ 0.65x $ from both sides: $$ 6.80 + 0.90x - 0.65x = 7.30 $$ $$ 6.80 + 0.25x = 7.30 $$ 2. Subtract $ 6.80 $ from both sides: $$ 0.25x = 7.30 - 6.80 $$ $$ 0.25x = 0.50 $$ 3. Divide both sides by $ 0.25 $: $$ x = \frac{0.50}{0.25} = 2 $$ Thus, the number of toppings needed for the pizzas to cost the same is $ \boxed{2} $.