Question 1201832: A large cheese pizza at palanzio’s pizzeria costs $6.80 plus $0.90 for each topping, while the cost of the large cheese pizza at guido’s pizza is $7.30 plus $0.65 for each topping. How many toppings needed to be added to the large cheese pizza from Palanzio’s pizzeria and Guido’s pizza for the pizzas to cost the same?
Answer by math_tutor2020(3817)   (Show Source):
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Answer: 2 toppings
Work Shown:
x = number of toppings
y = total cost
x is a nonnegative whole number 0,1,2,3,...
y is a positive real number
Palanzio's Pizzeria:
y = 0.90x + 6.80
Guido's Pizza
y = 0.65x + 7.30
We want the two costs (variable y) to be the same.
Apply substitution to solve for x.
y = 0.65x + 7.30
0.90x + 6.80 = 0.65x + 7.30
0.90x-0.65x = 7.30-6.80
0.25x = 0.50
x = 0.50/0.25
x = 2
We need to have 2 toppings for each pizza to arrive at the same cost for each.
As a check, let's plug x = 2 into each equation.
Palanzio:
y = 0.90x + 6.80
y = 0.90*2 + 6.80
y = 1.80 + 6.80
y = 8.60
Guido:
y = 0.65x + 7.30
y = 0.65*2 + 7.30
y = 1.30 + 7.30
y = 8.60
Each pizza place will charge $8.60 for two toppings.
This confirms the answer.
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