SOLUTION: In a group of 40 people the ratio of men to women is 3:1.how many women must join the group so that the ratio of men to women becomes 5:4?

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Question 990773: In a group of 40 people the ratio of men to women is 3:1.how many women must join the group so that the ratio of men to women becomes 5:4?
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39617) About Me  (Show Source):
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The group is initially 30 men and 10 women.

Adding the x more women does not change how many men.

%2830%29%2F%2810%2Bx%29=5%2F4

30=%28x%2B10%29%285%2F4%29
120=5%28x%2B10%29
120=5x%2B50
70=5x
highlight%28x=14%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
In a group of 40 people the ratio of men to women is 3:1.how many women must join the group so that the ratio of men to women becomes 5:4
Let m=numberof men in the original group of 40 people
(40-m)=numberof women in the original group of 40 people
m/(40-m)=3/1
120-3m=m
4m=120
m=30
40-m=w=10
let w=number of women to add to make to make the men/women ratio 5:4
numberof men in the original group of 40 people=30m
numberof women in the original group of 40 people=10w
30/(10+w)=5/4
50+5w=120
5w=70
w=14
how many women must join the group so that the ratio of men to women becomes 5:4? 14