Solve each problem by setting up and solving an appropriate system of equations.A college fraternity house spent $670 for an order of 85 pizzas.

Efan Halliday

Efan Halliday

Answered question

2021-09-04

Solve each problem by setting up and solving an appropriate system of equations.
A college fraternity house spent $670 for an order of 85 pizzas.
The order consisted of cheese pizzas, which cost $5 each, and Supreme pizzas, which cost $12 each.
Find the number of each kind of pizza ordered.

Answer & Explanation

Laith Petty

Laith Petty

Skilled2021-09-05Added 103 answers

Let the number of pizza C be x and the number of pizza S be y. We need to obtain two equations in two variables and then solve them to find x and y.
As the total number of pizzas is 85, so x+y=85. Also, the total cost of all the pizzas is $670, so 5x+12y=670.

Solve the equation x+y=85 for x by subtracting y from both the sides of the equation.
x+y=85

x=85y

Now, substitute x=85y in 5x+12y=670 and then solve for y as follows:

5(85y)+12y=670

4255y+12y670

7y=670425

y=2457

=35

 Now, substitute y=35 in x=85y and solve for x.

x=8535

=50

Therefore, the number of pizza C are 50 and the number of pizza S are 35.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-10-14Added 2605 answers

Answer is given below (on video)

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