Sure, I can help you with this question.
Let's define the variables:
Let x be the number of toppings added to the large cheese pizza at Palanzio’s Pizzeria.
Let y be the number of toppings added to the large cheese pizza at Guido’s Pizza.
Now let's write the system of equations:
The cost of the large cheese pizza at Palanzio’s Pizzeria is $6.80 plus $0.90 for each topping. So the equation for the cost at Palanzio’s Pizzeria can be written as:
Cost at Palanzio's Pizzeria = $6.80 + $0.90(x)
The cost of the large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. So the equation for the cost at Guido’s Pizza can be written as:
Cost at Guido's Pizza = $7.30 + $0.65(y)
We want to find the number of toppings that makes the cost equal at both restaurants. So we can set the two equations equal to each other and solve for the variable x:
$6.80 + $0.90(x) = $7.30 + $0.65(y)
Now we can solve for x. Here are the steps:
1. First, subtract $6.80 from both sides of the equation:
$0.90(x) = $7.30 + $0.65(y) - $6.80
$0.90(x) = $0.50 + $0.65(y)
2. Next, divide both sides of the equation by $0.90 to isolate x:
x = ($0.50 + $0.65(y)) / $0.90
x ≈ 0.56 + 0.72(y)
So the solution for x is x ≈ 0.56 + 0.72(y).
Now, the question asks for the number of toppings needed to make the pizzas cost the same. Since y is not given, we cannot find the exact number of toppings. However, we have expressed x in terms of y, so you can choose any value for y and find the corresponding value for x using the equation x ≈ 0.56 + 0.72(y).
I hope this helps! Let me know if you have any further questions.
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?
Alos, Can step-by-step bot help with this question?
1 answer