a = martinee
b = student
c = regular
All these ticked sold a total of 8500.
a+b+c = 8500
All of them also totaled $64600.
5a+6b+8.50c = 64600
And students tickets sold twice martinee tickets
b = 2a
a+2a+c = 8500
3a+c = 8500
Solve for the variable c
c = 8500 - 3a
And plug in the value
5a + 6(2a) + 8.5(8500-3a) = 64600
5a + 12a + 72250 - 25.5a = 64600
5a + 12a - 25.5a = 64600 - 72250
-8.5a = -7650
a can't be negative so multiply for -1 each side.
8.5a = 7650
solve for a and divide both for 8.5
8.5a/8.5 = 7650/8.5
a = 900 (martinee)
students are twice the martinee tickets
b = 2*900 = 1800 (student)
And to find regular subtract from 8500 (total) the unknown value of regular (3a)
c = 8500 - 3*900
c = 8500 - 2700
c = 5800 (regular)
