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?

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.

To find the percentage of people at the party who were married, we need to know the exact number of people in the room. Unfortunately, this information is not provided in the question. However, we can still determine the ratio of married people in the room.

Let's assume there are 100 people in the room as an example. If half the women are single, it means half of the women are married. Similarly, if 1/6 of the men are single, it means 5/6 of the men are married.

Let's break it down:

Number of women: 100 * 0.5 = 50 (assuming 50% of the total)

Number of men: 100 * (1 - 1/6) = 100 * (5/6) = 83.33 (rounded to 83 people)

Now, calculating the total number of married people:

Number of married women = 50 * 0.5 = 25 (assuming 50% of the women are married)

Number of married men = 83 * (5/6) = 69.17 (rounded to 69 people)

Total number of married people = 25 + 69 = 94 people

Finally, we can calculate the percentage of married people in the room:

Percentage of married people = (94 / 100) * 100 = 94%

Therefore, approximately 94% of the people at the party were married. Note that this percentage may vary depending on the actual number of people at the party.