SOLUTION: Tickets are available at 3 prices for a series of concerts. On a certain evening n people buys the cheapest tickets at x pounds. One third of this number buy the middle price ticke

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Question 697166: Tickets are available at 3 prices for a series of concerts. On a certain evening n people buys the cheapest tickets at x pounds. One third of this number buy the middle price ticket which costs 3 times as much as the cheapest and for every 5 sold for this price, 3 of the most expensive tickets are sold, each of which costs half of much again as the middle price ticket. In all, 690 people attend the concert paying a total of £1957.50. How many people buy the cheapest ticket and what is the cost of the most expensive ticket.
Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Revenues from the cheapest tickets is
(1) +n%2Ax+
Revenues from the middle price tickets is
(2) +%28n%2F3%29%2A%283x%29+
(2) +n%2Ax+
Revenues from the most expensive tickets is
(3) +%283%2F5%29%2A%28n%2F3%29%2A%283%2F2%29%2A%283x%29+
(3) +%289%2F10%29%2An%2Ax+
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given:
+n+%2B+n%2F3+%2B+%283%2F5%29%2A%28n%2F3%29+=+690+
+n+%2B+n%2F3+%2B+n%2F5+=+690+
+15n+%2B+5n+%2B+3n+=+690+
+23n+=+690+
+n+=+30+
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30 people buy the cheapest ticket
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given:
+1957.5+=+n%2Ax+%2B+n%2Ax+%2B+%289%2F10%29%2An%2Ax+
+1957.5+=+%2820%2F10%29%2An%2Ax+%2B+%289%2F10%29%2An%2Ax+
+1957.5+=+2.9%2An%2Ax+
+1957.5+=+2.9%2A30%2Ax+
+x+=+1957.5+%2F+87+
+x+=+22.5+
What is the cost of the most expensive ticket?
+%289%2F2%29%2Ax+=+%289%2F2%29%2A22.5+
+%289%2F2%29%2Ax+=+101.25+
The cost of most expensive ticket is 101.25 pounds
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check answers:
(1) +n%2Ax+=+30%2A22.5+
(1) +n%2Ax+=+675+
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(2) +n%2Ax+=+675+
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(3) +%289%2F10%29%2An%2Ax+=+.9%2A30%2A22.5+
(3) +%289%2F10%29%2An%2Ax+=+607.5+
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+2%2A675+%2B+607.5+=+1350+%2B+607.5+
+2%2A675+%2B+607.5+=+1957.5+
OK