Math problem riddle

Question

10 children equals 1 cent a woman costs 2 cent and a man costs 5 cents the theater made 1 dollar and all the people equaled 100

Answer 1

C+W+M = 100

C/10+2W + 5M = 100

multiply by 10

C+20W +50M = 1000

C + W + M = 100

19W + 49M = 900

two equations three unknowns should lead to an infinite number of possibilities

however, there's one additional constraint, C, W, and M have to be integers

which should narrow it down to, if not a unique solution, at least not that many solutions

Number of Children =70

Number of Women =19

Numbe of Men = 11

70+19+11= 100

70/10 + 2(19)+5(11) = 7+38+55 = 100

any other solutions give fractional persons or negative persons