Question

the panthers, a high school basketball team, charges $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?
○ there were 36 children at the game.
○ there were 50 children at the game.
○ there were 84 children at the game.
○ there were 108 children at the game.

Explanation:

Step1: Define variables

Let \( x \) be the number of adult tickets and \( y \) be the number of children's tickets. We know two equations:

1. The total number of people: \( x + y = 120 \) (so \( x = 120 - y \))
2. The total earnings: \( 6x + 3y = 612 \)

Step2: Substitute \( x \) into the earnings equation

Substitute \( x = 120 - y \) into \( 6x + 3y = 612 \):
\[
6(120 - y) + 3y = 612
\]

Step3: Expand and simplify

Expand the left - hand side: \( 720-6y + 3y=612 \)
Combine like terms: \( 720 - 3y=612 \)
Subtract 720 from both sides: \( - 3y=612 - 720=-108 \)

Step4: Solve for \( y \)

Divide both sides by - 3: \( y=\frac{- 108}{-3}=36 \)

Answer:

There were 36 children at the game.