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.

Question

x+ y= 24

3.50x + 5.00y = 97.50

Solve the system of equations. How many 10 oz. boxes were sold?

6
9
12
15

Answer 1

To solve the system of equations given, we have:

1. \(x + y = 24\) (Equation 1)
2. \(3.50x + 5.00y = 97.50\) (Equation 2)

where \(x\) is the number of 10 oz. boxes sold, and \(y\) is the number of 16 oz. boxes sold.

Let's solve Equation 1 for \(y\):

\[ y = 24 - x \]

Now, substitute \(y\) into Equation 2:

\[ 3.50x + 5.00(24 - x) = 97.50 \]

Distributing the \(5.00\):

\[ 3.50x + 120 - 5.00x = 97.50 \]

Combine like terms:

\[ -1.50x + 120 = 97.50 \]

Now, isolate \(x\):

\[ -1.50x = 97.50 - 120 \]

\[ -1.50x = -22.50 \]

Dividing both sides by \(-1.50\):

\[ x = \frac{-22.50}{-1.50} = 15 \]

Now that we have \(x\), we can find \(y\):

\[ y = 24 - x \]

\[ y = 24 - 15 = 9 \]

Thus, Jillian sold 15 boxes of 10 oz. cookies and 9 boxes of 16 oz. cookies. The answer to the question, "How many 10 oz. boxes were sold?" is:

15