Question 1057036
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)