Question

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket? please show work.

Answer 1

Assign variables to the groups. "S" stands for senior citizens and "C" stands for children. 


3S + 9C = 75

8S + 5C = 67

We must cancel one of these variables out; I did this by multiplying the top equation by 8 and the bottom equation by 3.

24S + 72C = 600
24S + 15C = 201

Subtract these two expressions and you get C = 7. Plug 7 in for C into any of the above expressions and solve for S. You will find that S = 4.