first thing I do is to multiple all the prices and revenue by 10. it avoids having to work with decimal numbers.
let's be A,B and C the numbers of seats for the tickets costing respectively 12$, 18$ and 24$
we have 12A + 18B + 24C = 10,200
and A + B + C = 600
we know that 1/3 of the tickets sold were at 18$, so 200 seats for a revenue of 200*18$ = 3600
we can replace in our equations
12A + (200*18) + 24C = 10,200
12A + 3,600 + 24C = 10,200
12A + 24C = 10,200 - 3,600
12A + 24C = 6,600
and A + B + C = 600
A + C = 400 therefore A = 400 - C
we can replace in the first equation
12(400 - C) + 24C = 6,600
4,800 - 12C + 24C = 6,600
12C = 1800
C = 150
answer is A
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