document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #845234 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "At a party, married people came with their husbands or wives.
\n" ); document.write( "If half of the women and 1/6 of the men in the party were single,
\n" ); document.write( "what percentage of the people in the room were married?
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document.write( "Let the number of married men at the party be x.\r\n" );
document.write( "Then the number of married women at the party is x, also,\r\n" );
document.write( "since married people came with their husbands or wives.\r\n" );
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document.write( "Then the number of single women at the party is x (same as the number of married women).\r\n" );
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document.write( "Now let's find the total number of men at the party, \"m\", in terms of x.\r\n" );
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document.write( "For this number m, we have this equation\r\n" );
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document.write( "     = ,  or\r\n" );
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document.write( "     =   -->  6(m-x) = m  -->  6m - 6x = m  -->  6m-m = 6x  -->  5m = 6x  -->  m = 6x/5.\r\n" );
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document.write( "So, the number of married   people at the party is  x + x = 2x;\r\n" );
document.write( "    the total number of the people at the party is  \r\n" );
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document.write( "     total   married  single\r\n" );
document.write( "      men     women   women\r\n" );
document.write( "      +    x    +  x  =   2x +  = .\r\n" );
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document.write( "Thus the ratio    is \r\n" );
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document.write( "     = cancel x in the numerator and denominator =  =  =  =  = 0.625,  or 62.5%.\r\n" );
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document.write( "ANSWER.  62.5% of the people in the room were married.\r\n" );
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