in a group of 180 person composed of men, women and children there are twice as many men as women and three times as many women as children. how many are there each?

Answer 1

number of men --- m
number of women --- w
number of children --- c
m+w+c = 180 , #1

m = 2w , #2

w = 3c , #3

from #2 , w = m/2
then in #3,
3c = w
c = (1/3)w = (1/3)(m/2) = m/6

back in #1
m+w+c = 180
m + m/2 + m/6 = 180
times 6
6m + 3m + m = 1080
10m= 1080
m = 108
then w = m/2 = 54
c = m/6 = 18

108 men, 54 women, and 18 children

check:
are there twice as many men as women? YES
are there three times as many women as children? YE
Are there 180 in total? YES
All is good!