SOLUTION: I need help setting up this problem please. Tickets to a recital cost $2.00 for children, $5.00 for adults and $3.00 for seniors citizens. After the recital, the organizers find

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Question 261062: I need help setting up this problem please.
Tickets to a recital cost $2.00 for children, $5.00 for adults and $3.00 for seniors citizens. After the recital, the organizers find that 570 people attended, and $1,950 was earned from ticket sales.However,they are unable to find a record of exactly how many children,adults,and senior citizens attended. All they can find is a cryptic note from the theater manager stating that three-fourths as many senior citizens as children attended
Found 2 solutions by solver91311, rfer:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the number of children

Let represent the number of adults

Let represent the number of seniors

We know that:



We also know that:



And finally we know that:



Solve the system. I would use the substitution method initially to reduce the system to two equations in two variables.

John

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
C+.75C+A=570
1.75C+A=570
A=570-1.75C
-----------------
2C+3(.75C)+5A=1950
--------------------
2C+2.25C+5(570-1.75C)
2C+2.25C+2850-8.75C=1950
-4.5C=-900
C=225 Children
.75C=169 Seniors
A=176 Adults