-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?
show steps in order
Let's represent the number of toppings as 'x'.
For Palanzio’s Pizzeria:
Cost of large pizza = $6.80
Cost of each topping = $0.90
Total cost = $6.80 + ($0.90 * x)
For Guido’s Pizza:
Cost of large pizza = $7.30
Cost of each topping = $0.65
Total cost = $7.30 + ($0.65 * x)
We need to find the value of 'x' for which both total costs are equal. So we set up the equation:
$6.80 + ($0.90 * x) = $7.30 + ($0.65 * x)
Now, let's solve for 'x'.
$6.80 + $0.90x = $7.30 + $0.65x
Subtract $0.65x from both sides:
$6.80 + $0.90x - $0.65x = $7.30 + $0.65x - $0.65x
$6.80 + $0.25x = $7.30
Subtract $6.80 from both sides:
$6.80 + $0.25x - $6.80 = $7.30 - $6.80
$0.25x = $0.50
Divide both sides by $0.25:
$0.25x / $0.25 = $0.50 / $0.25
x = 2
Therefore, in order for the pizzas to cost the same, 2 toppings need to be added to a large cheese pizza from Palanzio’s Pizzeria and Guido’s Pizza.