Question

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 the tax?

Answer 1

Let's begin by assigning a letter to represent our unknown:    x = # of toppings to be added to each pizza Now let's come up with expressions for the cost of each pizza with its toppings:    Palanxio's Pizza:  6.80 + 0.90x    Guido's Pizza:  7.30 + 0.65x Now let's equate the costs of both pizzas and solve for our unknown (x):    6.80 + 0.90x = 7.30 + 0.65x    0.90x - 0.65x = 7.30 - 6.80    0.25x = 0.50    x = 0.50/0.25    x = 2 toppings to be added to each pizza Finally, we can verify our answer by plugging it back into our equation and see if both costs are the same:    6.80 + 0.90x = 7.30 + 0.65x       [equation]    6.80 + 0.90(2) = 7.30 + 0.65(2)  [answer plug-in]    6.80 + 1.80 = 7.30 + 1.30    $8.60 = $8.60  [both costs are the same] Since both costs are the same, we are confident that our answer is correct.

Answer 2

For Palanzio’s Pizzeria and Guido’s Pizza to cost the same, the number of toppings needed is 2.

Let x represent the number of toppings and y represent the total money for large pizza at Palanzio’s Pizzeria. Since A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping, hence:

y = 0.9x + 6.80

Let x represent the number of toppings and z represent the total money for large pizza. Since A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping at Guido’s Pizza, hence:

z = 0.65x + 7.30

For both to cost the same, hence:

y = z

0.9x + 6.8 = 0.65x + 7.3

0.25x = 0.5

x = 2

For Palanzio’s Pizzeria and Guido’s Pizza to cost the same, the number of toppings needed is 2.

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