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 shown.
$x + y = 24$
$3.50x + 5.00y = 97.50$
solve the system of equations. how many 10 oz. boxes were sold?
6
12
15
9

Explanation:

Step1: Solve for \( y \) from the first equation

From \( x + y = 24 \), we can express \( y \) as \( y = 24 - x \).

Step2: Substitute \( y \) into the second equation

Substitute \( y = 24 - x \) into \( 3.50x + 5.00y = 97.50 \):
\[

$$\begin{align*} 3.50x + 5.00(24 - x) &= 97.50\\ 3.50x + 120 - 5.00x &= 97.50\\ -1.50x + 120 &= 97.50\\ -1.50x &= 97.50 - 120\\ -1.50x &= -22.50\\ x &= \frac{-22.50}{-1.50}\\ x &= 15 \end{align*}$$

\]

Answer:

15