Question 1207384
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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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<pre>
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

    {{{single_men/total_men}}} = {{{1/6}}},  or

    {{{(m-x)/m}}} = {{{1/6}}}  -->  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
     {{{(6x)/5}}} +    x    +  x  =   2x + {{{(6x)/5}}} = {{{(16x)/5}}}.


Thus the ratio  {{{married_people/total_people}}}  is 

    {{{((2x)/((16x)/5))}}} = cancel x in the numerator and denominator = {{{2/((16/5))}}} = {{{(2*5)/16}}} = {{{10/16}}} = {{{5/8}}} = 0.625,  or 62.5%.


<U>ANSWER</U>.  62.5% of the people in the room were married.
</pre>

Solved.