Question 1207384: At a party, married people came with their husbands or wives. If half of the women and 1/6 of the men in the party were single, what percentage of the people in the room were married?
Found 2 solutions by ikleyn, mccravyedwin:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
At a party, married people came with their husbands or wives.
If half of the women and 1/6 of the men in the party were single,
what percentage of the people in the room were married?
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Let the number of married men at the party be x.
Then the number of married women at the party is x, also,
since married people came with their husbands or wives.
Then the number of single women at the party is x (same as the number of married women).
Now let's find the total number of men at the party, "m", in terms of x.
For this number m, we have this equation
 =  , or
 = --> 6(m-x) = m --> 6m - 6x = m --> 6m-m = 6x --> 5m = 6x --> m = 6x/5.
So, the number of married people at the party is x + x = 2x;
the total number of the people at the party is
total married single
men women women
 + x + x = 2x + =  .
Thus the ratio  is
 = cancel x in the numerator and denominator =  =  =  =  = 0.625, or 62.5%.
ANSWER. 62.5% of the people in the room were married.
Solved.
Answer by mccravyedwin(407)  (Show Source):
You can put this solution on YOUR website!
The number of men must be a multiple of 6. So let there be 6N men.
1/6 of 6N men or 1N men are single and the other 5N men are married.
So 5N women are married to those 5N men, and since 1/2 the women are
single, 1/2 the women, or 5N are married, so another 5N women are single.
So the ratio of married to total people is
Edwin
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