SOLUTION: a jazz concert brought in $178000 on the sale of $8600 tickets. if the tickets sold for $15 each and $25 each, how many of each type of ticket were sold

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Question 1147770: a jazz concert brought in $178000 on the sale of $8600 tickets. if the tickets sold for $15 each and $25 each, how many of each type of ticket were sold
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of $15 tickets sold
Let +b+ = number of $25 tickets sold
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(1) +a+%2B+b+=+8600+
(2) +15a+%2B+25b+=+178000+
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(2) +3a+%2B+5b+=+35600+
Multiply both sides of (1) by 5
and subtract (2) from (1)
(1) +5a+%2B+5b+=+43000+
(2) +-3a+-+5b+=+-+35600+
-----------------------------------
+2a+=+7400+
+a+=+3700+
and
(1) +3700+%2B+b+=+8600+
(1) +b+=+4900+
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3700 $15 tickets sold
4900 $25 tickets sold
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check:
(2) +15a+%2B+25b+=+178000+
(2) +15%2A3700+%2B+25%2A4900+=+178000+
(2) +55500+%2B+122500+=+178000+
(2) +178000+=+178000+
OK