Answer:
[tex][/tex] Let's represent the total number of women and men in the meeting with the variables w and m, respectively.
We know that the number of women is equal to the number of men, so w = m.
We also know that two-fifths of the women wear glasses, so the number of women who wear glasses is [tex]\frac{2}{5}[/tex] [tex] \times[/tex] w.
And half of the women who wear glasses have long hair, so the number of women who wear glasses and have long hair is [tex]\frac{1}{2}[/tex] ( [tex]\frac{2}{5}[/tex] [tex] \times[/tex] w) = [tex]\frac{1}{5}[/tex] [tex] \times[/tex] w.
We are given that there are four women who wear glasses and have long hair, so [tex]\frac{1}{5}[/tex] [tex] \times[/tex] w = 4.
Solving for w, we get w = 20.
Since w = m, there are also m = 20 men in the meeting.
Therefore, the answer is 20.