Question

Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below. x y

Answer 1

Answer:

Jillian sold 15 ten-oz bags and 9 sixteen-oz bags.

Step-by-step explanation:

Let x represent number of 10-oz bags and y represent number of 16-oz bags.

We have been given that Jillian sold 24 boxes of cookies in total. We can represent this information in an equation as:

$x+y=24...(1)$

We are also told that 10 oz. box costs $3.50, while the 16 oz. box costs $5.00, so the cost of x 10-oz bags would be $3.50x$ and cost of y 16-oz bags would be $5y$.

At the end of one week, she collected $97.50. We can represent this information in an equation as:

$3.5x+5y=97.50...(2)$

Now, we will use substitution method to solve our system of equations. From equation (1), we will get:

$y=24-x$

Substitute this value in equation (2):

$3.5x+5(24-x)=97.50$

$3.5x+120-5x=97.50$

$-1.5x+120=97.50$

$-1.5x+120-120=97.50-120$

$-1.5x=-22.5$

$\frac{-1.5x}{-1.5}=\frac{-22.5}{-1.5}$

$x=15$

Therefore, the number of 10-oz boxes sold be Jillian is 15.

Now, we will substitute $x=15$ in equation (1) to solve for y.

$15+y=24$

$15-15+y=24-15$

$y=9$

Therefore, the number of 16-oz boxes sold be Jillian is 9.