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So, back in high school I learned the algorithm I needed to use in order to solve this problem. Unfortunately, I haven't needed the algorithm since high school and now I can't remember what it is!

I have a few known values, but two unknown values. I need to find the unknown. Here are the known values:

  • Tickets Sold 176

  • Adult Ticket 53

  • Child Ticket 31

  • Total Gross Revenue $6875.17

I need to find how many adults and how many children there were. I know I can't get an accurate answer because some sales had a 6% tax applied, but a best guess is better than nothing.

Thanks in advance!

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    Are you sure about those values? Beause there's no way that summing up those chil$d$ren and adult tickets would leave you with cents in the total cash... Also, I don't think this is an algebraic geometry question.2012-11-09

2 Answers 2

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Assuming all the tickets had $6\%$ tax applied, a child's ticket gives $\$32.86$ and an adult ticket gives $\$56.18$. If they were all children, you would get $\$5783.36$. Each child converted to an adult brings in an additional $\$23.32$, so we need to convert $\frac {6875.17-5783.36}{23.32} \approx 46.81$ passengers to adults. If none of the tickets were taxed, we would need about $64.5$ adults. So your range is $47$ to $64$ adults.

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    This is what I couldn't $r$emembe$r$! Thank you ve$r$y much $f$or your answer.2012-11-09
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Number of passegers is $176$, number of childs is $c$ number of adults is $a$. Then

$176=a+c \\ 53a+31c=6875.17$

Solve for $a$ and $c$

-Edit- Is the total price correct?

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    you are right. Unfortunately, I can't fix the thing that's wrong: the system in use.2012-11-09