there 90 men and 30 women in the class
Step-by-step explanation:The question isn't very clear. We woud be assuming:
The total number of men and women in the class = 120
The variables:
let the total number of men = m
let the total number of women = w
fraction of men with beards = three fifth = 3/5 of m
fraction of men without beards = 1 - 3/5 = 2/5 of m
fraction of women with long hair = 2/3 of w
fraction of women without long hair = 1- 2/3 = 1/3 of w
We are told 46 of them are not in the group stated above. We will take it as 46 men and women are not in the group above.
This means the fraction of men without beards and fraction of women without long hair are altogether = 46
46 = 2/5 of m + 1/3 of w
46 = 2m/5 + w/3 ....equation 1
The number of men and women in the group = 120 -46 = 74
74 = 3/5 of m + 2/3 of w
74 = 3m/5 + 2w/3 ....equation 2
Multiply equation 1 by 2:
92 = 4m/5 + 2w/3 ....equation 1
74 = 3m/5 + 2w/3 ....equation 2
subtract equation 2 from 1:
92 - 74 = 4m/5 - 3m/5 + 2w/3 - 2w/3
18 = m/5
5(18) = m
m = 90
Substitute the value of m in any of the equation. Using equation 2:
74 = 3(90)/5 + 2w/3
74 = 54 + 2w/3
74 - 54 = 2w/3
20 = 2w/3
cross multiply:
3(20) = 2w
60 = 2w
60/2 = w
w = 30
Therefore, there 90 men and 30 women in the class