PLEASE HELP!! ALGEBRA! For a movie theater 4,000 tickets were sold, and the proceeds were $37,000. Tickets for children 16 and younger, were $10, adults were $12, and seniors 60 and older were $8. There were 4 times more seniors than adults at the movie theater. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the movie theater?

Fourth answer choice

c+a+s = 4000

10c+12a+8s = 37000

4a = s

Explanation:

The first equation

c+a+s = 4000

is fairly straightforward. We add the individual counts of children (c), adults (a) and seniors (s) to get the total number of people (4000) who attended

If 1 child ticket costs $10, then 2 of them cost 20, and so on. If we don't know how many children there are, then we say 10c is the total cost for just the children alone. The c is a placeholder for some number.

Similarly, 12a represents the total cost for just the adults since 1 adult pays $12

8s is the total cost for all the seniors only

10c+12a+8s is the total cost of everyone and this total cost is 37000 dollars

The second equation is therefore

10c+12a+8s = 37000

We're told that "There were 4 times more seniors than adults at the movie theater" meaning

number of seniors = 4*(number of adults)

s = 4a

which is the same as 4a = s since we can flip both sides. So this is the third equation of our system.

We found these three equations

c+a+s = 4000

10c+12a+8s = 37000

4a = s

∠cbe and ∠deb are same-side interior angles.

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