Question

Restaurant has 100 seats capacity and so only 100 people can come in, there must be children, women, and men to complete 100 people. Restaurant can make only $100, each child pay 5 cent, woman pay $1 each, and man pay $5 each. How many men, women and children to make $100

Answer 1

Let c, w, m represent the number of children, women, and men, respectively.
c + w + m = 100........equation 1
.05c + w + 5m = 100........equation 2
Isolate w in equation 1:
w = 100 - c - m
And substitute into equation 2:
.05c + (100 - c - m) + 5m = 100
Simplify to get:
4m = .95c
Multiply both sides by 100:
400m = 95c
m/c = 95/400
m/c = 19/80
So the ratio of men to children is 19 to 80.
19 men and 80 children are the only possibilities here that add to a number under 100. Since these add to 99, there must be 1 woman.
So there are 80 children, 1 woman, and 19 men.