document.write( "Question 516355: a man is four years older than his wife and 5 times as old as his son.when the son was born the age of the wife is six-seventh of her husband's age.find the age of his wife. \n" ); document.write( "

Algebra.Com's Answer #344564 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( ">>...a man is four years older than his wife...<< \r\n" );
document.write( "\r\n" );
document.write( "M = W + 4\r\n" );
document.write( "\r\n" );
document.write( ">>...a man is...5 times as old as his son...<<\r\n" );
document.write( "\r\n" );
document.write( "M = 5S\r\n" );
document.write( "\r\n" );
document.write( ">>...when the son was born...<<\r\n" );
document.write( "\r\n" );
document.write( "That was S years ago when\r\n" );
document.write( "\r\n" );
document.write( "the man's age was M-S and the wife's age was W-S \r\n" );
document.write( "\r\n" );
document.write( "the age of the wife was six-seventh of her husband's age.\r\n" );
document.write( "\r\n" );
document.write( "Therefore W-S = (M-S)\r\n" );
document.write( "\r\n" );
document.write( "So we have the system of equations:\r\n" );
document.write( "\r\n" );
document.write( "M = W + 4\r\n" );
document.write( "M = 5S\r\n" );
document.write( "W-S = (M-S)\r\n" );
document.write( "\r\n" );
document.write( "Simplifying the third equation\r\n" );
document.write( "\r\n" );
document.write( "   7(W - S) = 6(M - S)\r\n" );
document.write( "    7W - 7S = 6M - 6S\r\n" );
document.write( "7W - S - 6M = 0\r\n" );
document.write( "\r\n" );
document.write( "M = W + 4\r\n" );
document.write( "M = 5S\r\n" );
document.write( "7W - S - 6M = 0\r\n" );
document.write( "\r\n" );
document.write( "Solving that system gives \r\n" );
document.write( "\r\n" );
document.write( "M = 35, W = 31,  S = 7\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );