To solve this problem, we need to understand the initial and final conditions of the committee's composition in terms of men and women.
Initial Condition:
The ratio of men to women in the committee is 3:1. This means for every 3 men, there is 1 woman. In a 20-member committee, let's determine the actual number of men and women.
Let the number of men be 3x and the number of women be x. According to the problem, the sum of men and women is 20:
3x + x = 20
Simplify this equation:
4x = 20
Divide both sides by 4 to find x:
x = 5
This means there are 3x = 3 * 5 = 15 men and x = 5 women in the committee.
Final Condition:
We want to add a certain number of women to change the ratio of men to women to 3:2. Let y be the number of women added.
Now, the number of women becomes 5 + y. The number of men remains 15.
The new ratio is:
Men : Women = 15 : (5 + y) = 3 : 2
Set up the equation based on the new ratio:
15/(5 + y) = 3/2
Cross-multiply to solve for y:
2 * 15 = 3 * (5 + y)
30 = 15 + 3y
Subtract 15 from both sides:
15 = 3y
Divide both sides by 3 to find y:
y = 5
Conclusion: Therefore, 5 women must be added to the committee to make the ratio of men to women 3:2.