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

Let x be the number of toppings added to a large cheese pizza from Palanzio's Pizzeria.

Let y be the number of toppings added to a large cheese pizza from Guido's Pizza.

The cost of a large cheese pizza from Palanzio's Pizzeria is 6.80 + 0.90x.
The cost of a large cheese pizza from Guido's Pizza is 7.30 + 0.65y.

We want to find the values of x and y such that the two costs are equal, so we can set up the following equation:

6.80 + 0.90x = 7.30 + 0.65y

To solve this equation, we can start by subtracting 7.30 from both sides:

6.80 + 0.90x - 7.30 = 0.65y

Simplifying, we get:

-0.50 = 0.65y - 0.90x

Next, we can rearrange the equation to isolate y:

0.65y = 0.90x - 0.50

Finally, we divide both sides by 0.65 to solve for y:

y = (0.90x - 0.50) / 0.65

So, the number of 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 is (0.90x - 0.50) / 0.65.