Question

The number of boys varies directly as the number of girls and inversely as the number of teachers when there are 24 boys and 16 girls there are 2 teachers how many girls are there when there are 73 boys and 1 teacher?

Answer 1

Let the number of boys be b, the number of girls be g and that of teachers be t,
thus:
b=kg/t
where k is the constant of proportionality
k=bt/g
b=24, when g=16 and t=2
k=(24*2)/16
k=3
hence:
b=(3g)/2
thus the number of girls when:
b=73 and t=1 will be:
73=(3*g)/1
73=3g
g=73/3
g=24.333~ 24 girls