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's assume that the number of toppings added to the large cheese pizza from Palanzio's Pizzeria is x, and the number of toppings added to the large cheese pizza from Guido's Pizza is y.
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.
To find the number of toppings needed for the pizzas to cost the same, we need to set the costs equal to each other and solve for the variables:
6.80 + 0.90x = 7.30 + 0.65y
Subtracting 0.65y and subtracting 6.80 from both sides:
0.90x - 0.65y = 7.30 - 6.80
0.90x - 0.65y = 0.50
To solve this problem, we need another equation. Let's use the fact that the total number of toppings on the pizzas must be the same. Since x represents the number of toppings on the pizza from Palanzio's Pizzeria and y represents the number of toppings on the pizza from Guido's Pizza, we can write the equation:
x = y
Now we have a system of equations:
0.90x - 0.65y = 0.50
x = y
To solve this system, we can substitute x = y into the first equation:
0.90(y) - 0.65y = 0.50
0.90y - 0.65y = 0.50
0.25y = 0.50
Divide both sides by 0.25:
y = 2
Since x = y, the number of toppings needed for the pizzas to cost the same is also 2.