Let's denote the number of toppings as \( x \).
The total cost of a large pizza at Palanzio’s Pizzeria can be expressed as: \[ C_p = 6.80 + 0.90x \]
The total cost of a large cheese pizza at Guido’s Pizza can be expressed as: \[ C_g = 7.30 + 0.65x \]
To find out how many toppings \( x \) make the costs equal, we set the two cost expressions equal to each other: \[ 6.80 + 0.90x = 7.30 + 0.65x \]
Now, we will solve for \( x \). First, subtract \( 0.65x \) from both sides: \[ 6.80 + 0.90x - 0.65x = 7.30 \] This simplifies to: \[ 6.80 + 0.25x = 7.30 \]
Next, 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, the number of toppings needed for the large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza to cost the same is \( \boxed{2} \).
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