Answer: Fourth answer choice
c+a+s = 4000
10c+12a+8s = 37000
4a = s
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Step-by-step 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
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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
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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.
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We found these three equations
c+a+s = 4000
10c+12a+8s = 37000
4a = s