# Linear Algebra Word Question (school play audience numbers and ticket prices)

A school play ran for two nights, with audiences totaling 1390 adults and students. They paid 4285 dollars for admission. One adult ticket cost 4 dollars and one student ticket cost 2.50 dollars. The ratio of adults to students was 3:5 for the first night and 2:3 on the second night. How many students attended each night?

I have determined that there was 850 students and 540 adults on both nights, but for the life of me couldn't figure out how to incoporate those ratios into finding how much students were per day.

This is marked as a homework question so please don't give me the full answer but how to go about it. I also have the answers if that is any help: for the first night, there were 400 students on the first night, and 450 on the second.

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I have verified that the adult/student totals you got is correct.

For the second part:

Suppose a total of $x$ people (i.e. including students and adults) attended the first day and total $y$ people attended the second day.

What is the total number of students in terms of $x$ and $y$?

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One more hint please? It seems to me that I'm back where I started if I do that. – highy Oct 5 '10 at 1:23
@high: Do the same with number of adults. You have 2 variables, 2 equations. I believe you already know how to solve that. – Aryabhata Oct 5 '10 at 1:23
Still stuck. I figured out that on the first night, there would be 240 adults and then 300 on the second day, but I'm still unsure how it all fits together... – highy Oct 5 '10 at 2:02
So if you have the number of adults each night (which I have not verified) the ratios give the number of students – Ross Millikan Oct 5 '10 at 2:14
@Moron- That was so obvious I can't believe I didn't see that. I keep thinking about the ratios.... Well, thanks, I got the answer! Thanks for wasting your time with me :) – highy Oct 5 '10 at 14:46