The formula to determine the total money is
nA + mC = 1317.50
where n is the number of adult tickets sold and A is the price of the adult tickets and m OS the number of child tickets and C is the price of a child ticket.
Substituting in the actual prices we get...
eq 1. n*7.50 + m * 3.50 = 1317.50
eq 2. n+m = 205
rearranging eq 2 we get
n = 205 - m
substituting this into eq 1 we get..
(205 -m) * 7.5 + m * 3.5 = 1317.50
Simplifying we get
1537.5 - 7.5m + 3.5m = 1317.50
1537.5 - 1317.5 = 4m
220 = 4m
55 = m
substituting into eqn 2 we get
n + 55 = 205
n = 150.
Therefor
150 Adult tickets were sold
55 Child tickets were sold