Question

tickets for a high school basketball game cost $4 for adults and $3 for students. the school sells 120 tickets and makes $412 in ticket sales. the system of equations shown can be used to determine the number of adult tickets a and the number of student tickets s that the school sold. \

$$\begin{cases} a + s = 120 \\\\ 4a + 3s = 412 \\end{cases}$$

how many adult tickets and how many student tickets did the school sell? enter the correct answers in the boxes. show hints \square adult tickets \square student tickets

Explanation:

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

From \( a + s = 120 \), we can express \( s \) as \( s = 120 - a \).

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

Substitute \( s = 120 - a \) into \( 4a + 3s = 412 \):
\[

$$\begin{align*} 4a + 3(120 - a) &= 412\\ 4a + 360 - 3a &= 412\\ a + 360 &= 412 \end{align*}$$

\]

Step3: Solve for \( a \)

Subtract 360 from both sides:
\[
a = 412 - 360 = 52
\]

Step4: Solve for \( s \)

Substitute \( a = 52 \) into \( s = 120 - a \):
\[
s = 120 - 52 = 68
\]

Answer:

52 adult tickets
68 student tickets