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?

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.