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.