Question

On Friday, a total of 135 tickets to the fall play were sold for s total amount of $634. Adult tickets are $6 each and student cost $4 each. How many students and adults attended the play last night?

Answer 1

88 students and 47 adults

Explanation:

Let x be the number of students and y be the number of adults attended the play last night.

1. A total of 135 tickets to the fall play were sold, then

`x+y=135`

2. A total amount of $634 waas earned.

Student ticket costs $4, then x student tickets cost $4x.

Adult ticket costs $6, then y adult tickets cost $6y.

In total,

`4x+6y=634`

3. Solve the system of two equations:

`\left\{\begin{array}{l}x+y=135\\4x+6y=634\end{array}\right.`

From the first equation,

`x=135-y`

Substitute it into the second equation,

`4(135-y)+6y=634\\ \\540-4y+6y=634\\ \\2y=634-540\\ \\2y=94\\ \\y=47\\ \\x=135-47=88`