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)](https://tex.z-dn.net/?f=x%2By%3D24...%281%29)
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
and cost of y 16-oz bags would be
.
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)](https://tex.z-dn.net/?f=3.5x%2B5y%3D97.50...%282%29)
Now, we will use substitution method to solve our system of equations. From equation (1), we will get:
![y=24-x](https://tex.z-dn.net/?f=y%3D24-x)
Substitute this value in equation (2):
![3.5x+5(24-x)=97.50](https://tex.z-dn.net/?f=3.5x%2B5%2824-x%29%3D97.50)
![3.5x+120-5x=97.50](https://tex.z-dn.net/?f=3.5x%2B120-5x%3D97.50)
![-1.5x+120=97.50](https://tex.z-dn.net/?f=-1.5x%2B120%3D97.50)
![-1.5x+120-120=97.50-120](https://tex.z-dn.net/?f=-1.5x%2B120-120%3D97.50-120)
![-1.5x=-22.5](https://tex.z-dn.net/?f=-1.5x%3D-22.5)
![\frac{-1.5x}{-1.5}=\frac{-22.5}{-1.5}](https://tex.z-dn.net/?f=%5Cfrac%7B-1.5x%7D%7B-1.5%7D%3D%5Cfrac%7B-22.5%7D%7B-1.5%7D)
![x=15](https://tex.z-dn.net/?f=x%3D15)
Therefore, the number of 10-oz boxes sold be Jillian is 15.
Now, we will substitute
in equation (1) to solve for y.
![15+y=24](https://tex.z-dn.net/?f=15%2By%3D24)
![15-15+y=24-15](https://tex.z-dn.net/?f=15-15%2By%3D24-15)
![y=9](https://tex.z-dn.net/?f=y%3D9)
Therefore, the number of 16-oz boxes sold be Jillian is 9.