Question

3/5 of the workers in a factory were men and the rest were women.
1/2 of the men and 1/4 of the women were foreigners and the rest were
Singaporeans. There were 138 Singaporeans. How many workers
were there in the factory?

Answer 1

let W equal workers

women Singaporeans ... W * (1 - 3/5) * (1 - 1/4) = 6/20 W = 3/10 W

men Singaporeans ... W * 3/5 * (1 - 1/2) = 3/10 W

3/10 W + 3/10 W = 3/5 W = 138

solve for W

Answer 2

Number of men --- m
number of women --- w
m : w = 3 : 2
3w = 2m
w = (2/3)m

"1/2 of the men and 1/4 of the women were foreigners and the rest were
Singaporeans"
so 1/2 of the men and 3/4 of the women were Singaporeans,
so (1/2)m + (3/4)w = 138
times 4:
2m + 3w = 552
use substitution
2m + 3(2/3)m = 552
4m = 552
m = 138
w = 92 , for a total of 230

check:
if 3/5 of 230 are men ---> 138 men, ✔
the rest = 230-138 = 92 , so 92 women, ✔
foreigners: 1/2 of men + 1/4 women
= 69 + 23 = 92
Singaporeans = total - 92 = 138 ✔

my answer is correct