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?
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.