Efan Halliday

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.

Laith Petty

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.
$x+y=85$

$x=85-y$

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

$5\left(85-y\right)+12y=670$

$425-5y+12y-670$

$7y=670-425$

$y=\frac{245}{7}$

$=35$

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

$x=85-35$

$=50$

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

Jeffrey Jordon