SOLUTION: Could you please help me with this problem? I have a hard time figuring out how to set up word problems... The Family Arts Center charges $21 for adults, $14 for Senior citizen

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Question 171693: Could you please help me with this problem? I have a hard time figuring out how to set up word problems...
The Family Arts Center charges $21 for adults, $14 for Senior citizens, and $5 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $9417 for 735 tickets sold. There were 43 more children than adults. How many children attended?
Thank you so much for your help...
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
What I do that really helps me is to
immediately assign letters for the
unknown quantities in the equation:
Let = the number of adults attending
Let = the number of Seniors attending
Let = the number of children attending
--------------
Now I can write equations
(1)
(2)
(3)
-------------
There are 3 equations and 3 unknowns, so it
should be solvable
Multiply (1) by and subtract (2) from (1)
(1)

Substitute (3)

Since (3) is given,

And, from (1)

286 children attended
check answer:
(2)

(1)

(3)

OK