Question

The Panthers, a high school basketball team, charge $6 for adult tickets and $3 for children's tickets. If 120 people went to the most recent game, and the total earnings for ticket sales was $612, how many children went to the game?(1 point)
Responses

There were 84 children at the game.
There were 84 children at the game.

There were 50 children at the game.
There were 50 children at the game.

There were 108 children at the game.
There were 108 children at the game.

There were 36 children at the game.

Answer 1

Let \( x \) be the number of adult tickets sold and \( y \) be the number of children's tickets sold. We can set up the following system of equations based on the information provided:

1. The total number of people:
\[
x + y = 120
\]

2. The total earnings from ticket sales:
\[
6x + 3y = 612
\]

Now, we can solve this system of equations. Start with the first equation:

\[
x = 120 - y
\]

Now substitute \( x \) in the second equation:

\[
6(120 - y) + 3y = 612
\]

Distributing the 6:

\[
720 - 6y + 3y = 612
\]

Combining like terms:

\[
720 - 3y = 612
\]

Subtract 720 from both sides:

\[
-3y = 612 - 720
\]
\[
-3y = -108
\]

Dividing both sides by -3:

\[
y = 36
\]

So, there were **36 children** at the game.

To find the number of adults, substitute \( y \) back into the first equation:

\[
x + 36 = 120
\]
\[
x = 84
\]

Thus, the number of adults is 84, and the number of children is confirmed to be 36.

Therefore, the answer is:
**There were 36 children at the game.**