Question

Really really need some help here.,

There was an I.T. Fair. 2/9 of the visitors were children. There were 4000 more adults than children. The ratio of boys to the number of girls was 3:5. The ratio of number of men to number of women was 3:1. Find the number of all male visitors in the IT Fair.

Answer 1

boys -- b
girls -- g

b/g = 3/5
5b = 3g
b = 3g/5 OR g = 5b/3

men --- m
women -- w
m/w = 3/1
m = 3w

equation #1:
2/9 of the visitors were children:
b+g = (2/9)( b+g+m+w)
9b + 9g = 2b + 2g + 2m + 2w)
7b + 7g = 2m + 2w
7(3g/5) + 7g = 6w + 2w
times 5
21g + 35g = 40w
56g = 40w -----> 20w = 28g *****
g = 5w/7

Equation #2
there were 4000 more adults than children
m+w = b+g + 4000
3w + w = 3g/5 + g + 4000
times 5
20w = 3g + 5g + 20000
20w = 8g + 20000
just notice above ****** that 20w = 28g
so
28g = 8g+20000
20g = 20000
g = 1000
b = 3g/5 = 600
from 20w = 28g
w = 1400
m = 4200
There were 4200 male visitors

This may not be the best or quickest way of doing that question, but I wanted to show how you can just "translate" the English into Math.


check:
2/9 of the visitors were children.
--> (2/9)(total) = 1600 , yes
There were 4000 more adults than children.
---> childdren = 1600 , adults = 5600, more by 4000? yes
The ratio of boys to the number of girls was 3:5
--? boys/girls = 600/1000 = 3/5 , yes
The ratio of number of men to number of women was 3:1
---> men/women = 4200/14/ = 3/1 , yes