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MariettaO [177]
3 years ago
11

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 cos

ts $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
Mathematics
1 answer:
RideAnS [48]3 years ago
8 0

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.

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