document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145748>Question 1145748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man is four years older than his wife and 5 times than his son. When the son was born, the age of wife is six-seventh that of the husband’s age. Find the age of the wife. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #767001 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=767001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i get the following solution.\r<BR>\n" );
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document.write( "the age of the man is 33.6<BR>\n" );
document.write( "the age of the wife is 29.6<BR>\n" );
document.write( "the age of the son is 5.6\r<BR>\n" );
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document.write( "the man is 4 years older than his wife (33.6 - 29.6 = 4)<BR>\n" );
document.write( "the man is 5 times older than his son ((33.6-5.6)/5.6 = 5)\r<BR>\n" );
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document.write( "when the son was born, the wife was 6/7 * the age of the man.<BR>\n" );
document.write( "29.6 - 5.6 = 24<BR>\n" );
document.write( "33.6 - 5.6 = 28<BR>\n" );
document.write( "24/28 = 6/7\r<BR>\n" );
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document.write( "you said \"and 5 times than his son\"<BR>\n" );
document.write( "i took that to mean \"5 times older than his son\"<BR>\n" );
document.write( "if that's not what you meant, than you need to clarify what you meant.\r<BR>\n" );
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document.write( "5 times older than his son means that that the father is 6 times as old as his son.\r<BR>\n" );
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document.write( "if you meant \"5 times as old as his son\", then the solution winds up being the same, but with different numbers as shown below.\r<BR>\n" );
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document.write( "the man is 35.<BR>\n" );
document.write( "the woman is 31.<BR>\n" );
document.write( "the son is 7 (5 * 7 = 35)\r<BR>\n" );
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document.write( "7 years ago, the son was born.<BR>\n" );
document.write( "the women was 31 - 7 = 24<BR>\n" );
document.write( "the man was 35 - 7 = 28<BR>\n" );
document.write( "24 / 28 = 6/7\r<BR>\n" );
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document.write( "the method of solution, assuming the man was 5 times as old as his son, was as follows:\r<BR>\n" );
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document.write( "let m = the age of the man<BR>\n" );
document.write( "let w = the age of the woman<BR>\n" );
document.write( "let s = the age of the son.\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "m = w + 4<BR>\n" );
document.write( "m = 5 * s<BR>\n" );
document.write( "since m = w + 4 and m = 5 * s, then you get w + 4 = 5 * s<BR>\n" );
document.write( "solve for s to get s = (w + 4) / 5\r<BR>\n" );
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document.write( "the son was born s years ago.<BR>\n" );
document.write( "when the son was born, the woman was 6/7 * the man's age.<BR>\n" );
document.write( "you get (w - s) = 6/7 * (m - s)<BR>\n" );
document.write( "multiply both sides of this equation by 7/6 and you get:<BR>\n" );
document.write( "7/6 * (w - s) = (m - s) which can also be shown as:<BR>\n" );
document.write( "(m - s) = 7/6 * (w - s)<BR>\n" );
document.write( "multiply both sides of this equation by 6 to get:<BR>\n" );
document.write( "6 * (m - s) = 7 * (w - s)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "6m - 6s = 7w - 7s\r<BR>\n" );
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document.write( "this last equation is used to solve the problem.<BR>\n" );
document.write( "start with 6m - 6s = 7w - 7s<BR>\n" );
document.write( "replace m with w + 4 and replace s with (w + 4) / 5 to get:<BR>\n" );
document.write( "6 * (w + 4) - 6 * (w + 4) / 5) = 7 * w - 7 * (w + 4) / 5<BR>\n" );
document.write( "multiply both sides of this equation by 5 to get:<BR>\n" );
document.write( "30 * (w + 4) - 6 * (w + 4) = 35 * w - 7 * (w + 4)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "30 * w + 120 - 6 * w - 24 = 35 * w - 7 * w - 28<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "24 * w + 96 = 28 * w - 28<BR>\n" );
document.write( "subtract 24 * w from both sides and add 28 to both sides to get:<BR>\n" );
document.write( "124 = 4 * w<BR>\n" );
document.write( "solve for w to get:<BR>\n" );
document.write( "w = 31\r<BR>\n" );
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document.write( "since m = w + 4, the m = 35<BR>\n" );
document.write( "since m = 5 * s, then s = 7\r<BR>\n" );
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document.write( "you get:<BR>\n" );
document.write( "m = 35<BR>\n" );
document.write( "w = 31<BR>\n" );
document.write( "s = 7\r<BR>\n" );
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document.write( "the son was born 7 years ago.<BR>\n" );
document.write( "the man was 28<BR>\n" );
document.write( "the woman was 24<BR>\n" );
document.write( "24/28 = 6/7\r<BR>\n" );
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document.write( "your solution, assuming that the man is 5 times as old as his son, is that the wife is 31 years old.\r<BR>\n" );
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document.write( "similar logic was applied if i assumed that the man was 6 times as old as his son.<BR>\n" );
document.write( "in that case, w + 4 = 6s which makes s = (w + 4) / 6.\r<BR>\n" );
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document.write( "assuming the man is 5 times as old as his son, rather than assuming the man is 5 times older than his son, gave me a cleaner answer.\r<BR>\n" );
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document.write( "that's why i'm thinking you meant 5 times as old as his son, rather than 5 times older than his son.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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