Question

At a party, married people came with their husbands or wives. if half the women and 1/6 of the men in the party were single, what percentage of the people in the room were married?

Answer 1

If there are
x married men (or women)
y single men
z single women,

we want 2x/(2x+y+z)

(x+z)/2 = z
(x+y)/6 = y

x = z
x = 5y
so, z = 5y

2x/(2x+y+z) = 2*5y/(2*5y+y+5y) = 10/16 = 62.5%

Check:
If 1 single man
5 single women
5 married couples

there were 16 people in the room. 10 are married

Naturally, any multiple of those numbers will also work.