At first,
75% = 75/100 = ¾

So ¾ of the dancers were women.

Ratio of women to men to total
= 3 : 1 : 4

Women at first ⬛⬛⬛
Men at first ⬛


After 33 women and 6 men left the hall,

Number of women in each group = 7 - 2 = 5

Ratio of men to women in all the groups combined to total = 2 : 5 : 7

Women ☆☆☆☆☆
Men ☆☆

From this we can realise two things :

Total women at first = ​⬛⬛⬛ = ☆☆☆☆☆ + 33

Total men at first = ⬛ = ☆☆ + 6


Since ⬛ = ☆☆ + 6,

⬛⬛⬛ =

☆☆ + 6
☆☆ + 6
☆☆ + 6

= ☆☆☆☆☆☆ + 18


Now compare this to the women equation :

☆☆☆☆☆☆ + 18
=
☆☆☆☆☆ + 33



☆ = 33 - 18 = 15

Number of people in the ballroon at first

= ☆☆☆☆☆☆☆ + 33 + 6
= 15 × 7 + 33 + 6
= 105 + 39
= 144