System of equations with three variables

Question

At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child's ticket was $20.50, an adult ticket was $29.75, and a senior citizen ticket was $15.25. There were twice as many senior citizens as adults in attendance, and 20 more children than senior citizens. How many children, adult and senior citizen tickets were sold? 

Answer 1

I will not solve this problem for you, but I will tell you how to do it.

Let C=# child tickets, A=# of adults and S=# seniors

20.50C + 29.75A + 15.25S = 2914.25

Hint: Before doing anything else, multiply this equation by 100 to get rid of the decimals!

S=2A

C=S+20=2A + 20

Now substitute the expressions for S and C in terms of A into the first equation, multiply and collect terms, then solve for A. Once you have A you can calculate S and C.