Question

-A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping.

How many toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza in order for the pizzas to cost the same, not including tax?

Answer 1

Let \( x \) be the number of toppings added to each pizza.

The total cost for a large pizza at Palanzio’s Pizzeria can be expressed as:

\[
\text{Cost at Palanzio’s} = 6.80 + 0.90x
\]

The total cost for a large cheese pizza at Guido’s Pizza can be expressed as:

\[
\text{Cost at Guido’s} = 7.30 + 0.65x
\]

To find out how many toppings need to be added so that the costs are equal, we set these two expressions equal to each other:

\[
6.80 + 0.90x = 7.30 + 0.65x
\]

Now we will solve for \( x \). First, we can simplify the equation by subtracting \( 0.65x \) from both sides:

\[
6.80 + 0.90x - 0.65x = 7.30
\]

This simplifies to:

\[
6.80 + 0.25x = 7.30
\]

Next, we subtract \( 6.80 \) from both sides:

\[
0.25x = 7.30 - 6.80
\]

\[
0.25x = 0.50
\]

Now, divide both sides by \( 0.25 \):

\[
x = \frac{0.50}{0.25} = 2
\]

Thus, **2 toppings** need to be added to a large cheese pizza from both Palanzio’s Pizzeria and Guido’s Pizza in order for them to cost the same.

To verify:

- Cost at Palanzio’s with 2 toppings:
\[
6.80 + 0.90(2) = 6.80 + 1.80 = 8.60
\]

- Cost at Guido’s with 2 toppings:
\[
7.30 + 0.65(2) = 7.30 + 1.30 = 8.60
\]

Both costs are indeed $8.60. Therefore, the solution is confirmed correct:

\[
\boxed{2}
\]