Question

At a local country club with 84 members, there are half as
many women as there are men. The next month, 8 women
join and the ratio of women to men is now 3 to 4. How
many men joined or left?
A. 20 left
B. 20 joined
C. 8 joined
D. 8 left​

Answer 1

Answer:

Answer is

B. 20 joined

Answer 2

Answer:

8 left

Explanation:

W + M = 84        eq1

W = M/2  or M = 2W         eq2

putting eq2 in eq1

W + 2W = 84

3W = 84

W = 28

finding M by putting w = 28 in eq1

28 + M = 84

M = 56

After 8 women joined, ratio became 3:4

28 + 8 / 56 + x  = 3 / 4 (let x be number of men who joined or left)

36 / 56 + x = 3 / 4

4(36) = 3(56 + x)

144 = 168 + 3x

144 - 168 = 3x

-24 = 3x

x = -8 (minus indicating 8 men left)