Word problem with many givens.

Question

Tickets sold at box office are $4.25 for children,$9.75 adult's & $5.50 for senior citizens. Each paid admission receives raffle ticket. Children receives 1 raffle ticket,senior citizen 2 & adults 3 raffle tickets. 1118 people attended total revenue was $8037.5. Total number of raffle tickets distributed was 2518. How many children, adults and senior citizens attended?

Answer 1

C + A + S =1118

4.25C + 9.75A + 5.50S = 8037.50

C + 3A + 2S = 2518

This simultaneous set of linear equations is a nuisance to solve. I will start; you finish.

Eliminate the C from the 3rd by subtracting the the first equation from the third: 2A + S = 1400.

Multiply the 2nd equation by 4: 17C + 39A + 22S = 32150.

Now multiply the first equation by 17 and eliminate the C from the 2nd equation by subtraction.

You will now have 2 simultaneous equations in A and S. Solve the set, then use the values of A and S to find C. Good luck!