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

Answer 1

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 \( \boxed{2} \).