SOLUTION: The family fine arts center charges $22 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 478 people paid admission, the total receipts we

Algebra ->  Linear-equations -> SOLUTION: The family fine arts center charges $22 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 478 people paid admission, the total receipts we      Log On


   

Question 1057036: The family fine arts center charges $22 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 478 people paid admission, the total receipts were $7376. if a represents the number of adults that attended, and s represents the number of senior citizens that attended, determine the number of senior citizens that attended by solving the following systems of equations. you may solve using any method you chose, but all work must be shown.
Found 2 solutions by jorel555, math_helper:
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
If a is adults, and s is for senior citizens, then:
22a+12s=7376
Since s=478-a, then:
22a+12(478-a)=7376
10a+5736=7376
10a=1640
a=164
There were 164 adults and 314 senior citizens. ☺☺☺☺

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
From the problem statement:
a + s = 478 (478 people paid admission) (1)
22a + 12s = 7376 (total receipts) (2)
(1) implies a = 478-s
Substitute this value for 'a' in (2):
22(478-s) + 12s = 7376
10516 - 22s + 12s = 7376
3140 - 10s = 0
3140 = 10s
314 = s
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Ans: s=314 ( 314 senior citizens attended ).
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Check:
s=314 tells us a = 478-314 = 164
Receipts = 314*12 + 164*22 = 7376 (ok)