Here is the question:

Question

At a local performance of "The Music Man," 966 tickets were sold. The total earnings for the performance was $9,348. Children tickets cost $9 each, adult tickets cost $12 each, and senior citizen tickets cost $6 each. If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 162, how many tickets of each tip were sold?

Answer 1

The answer is found using three equations and three unknowns, and substitution.

 

Let C = # of children's tickets sold

Let A = # of adult tickets sold

Let S = # of senior tickets sold

 

The three equations are the following:

 

1.)   C+A+S = 966

2.)   9C + 12A + 6S = 9348

3.)   C+A = 2S+162

 

To get started, solve for S by substituting (2S + 162) for (C+A) in equation 1.