SOLUTION: The Little Town Fine Arts Center carges $20 per adult and $15 per senior citizen for its performances. On a recent weekend evening when 493 people paid admission, the total receipt

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Question 514428: The Little Town Fine Arts Center carges $20 per adult and $15 per senior citizen for its performances. On a recent weekend evening when 493 people paid admission, the total receipts were &8210. How many who paid were senior citizens?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of adults
Let s = number of seniors
given:
(1) +a+%2B+s+=+493+
(2) +20a+%2B+15s+=+8210+
Multiply both sides of (1) by 15
and subtract (1) from (2)
(2) +20a+%2B+15s+=+8210+
(1) +-15a+-+15s+=+-7395+
+5a+=+815+
+a+=+163+
and, since
(1) +a+%2B+s+=+493+
(1) +163+%2B+s+=+493+
(1) +s+=+330+
330 were seniors
check answer:
(2) +20a+%2B+15s+=+8210+
(2) +20%2A163+%2B+15%2A330+=+8210+
(2) +3260+%2B+4950+=+8210+
(2) +8210+=+8210+
OK