Solving systems of equations word problems worksheet For all problems, define variables, write the system of equations and solve for all variables.

-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?

1 answer

Let's define:
x = number of toppings added to the large cheese pizza at Palanzio's Pizzeria
y = number of toppings added to the large cheese pizza at Guido's Pizza

The system of equations is:
Palanzio's Pizzeria: 6.80 + 0.90x
Guido's Pizza: 7.30 + 0.65y

To find the number of toppings needed for the pizzas to cost the same, we set the two equations equal to each other:
6.80 + 0.90x = 7.30 + 0.65y

Now, we can solve for x and y.
0.90x - 0.65y = 7.30 - 6.80
0.90x - 0.65y = 0.50

To get rid of the decimals, we can multiply both sides of the equation by 100:
90x - 65y = 50

Now, this equation can be solved further depending on the specific values of x and y that are desired.