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:
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Cost at Palanzio’s with 2 toppings: \[ 6.80 + 0.90(2) = 6.80 + 1.80 = 8.60 \]
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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:
\[ \boxed{2} \]
1 answer