SOLUTION: A theater sold 160 children’s tickets and 90 adult tickets. If the theater made $1,600 from the sales of the tickets, what were the prices of each ticket?

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Question 935070: A theater sold 160 children’s tickets and 90 adult tickets. If the theater made $1,600 from the sales of the tickets, what were the prices of each ticket?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
c for price of child ticket, g for price of grownup ticket.

160c%2B90g=1600 accounting for sales revenue.

16c%2B9g=160, and expect that c%3Cg.

16c=-9g%2B160
c=-%289%2F16%29g%2B10
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substitute into the inequality:
-%289%2F16%29g%2B10%3Cg
10%3Cg%2B%289%2F16%29g
160%3C16g%2B9g
160%3C25g
g%3E160%2F25
g%3E32%2F5 which is $6.40. This is a lower boundary for adult ticket price.

Now solve the equation for g instead; MAYBE it would help further(?).
9g=160-16c
g=160%2F9-%2816%2F9%29c
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substitute to the inequality,
c%3Cg
c%3C160%2F9-%2816%2F9%29c
9c%3C160-16c
9c%2B16c%3C160
25c%3C160
c%3C160%2F25, which is the same boundary as for adult price, but just in the other direction.

As finely grained as you can find solutions, the ticket prices MUST be in whole penny quantities, including 0. Children's tickets are priced as BELOW $6.40, and adult tickets are HIGHER than $6.40. Several solutions to the two dimensional problem are possible as long as you take perfect hundredth of a dollar accuracy.