document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118139>Question 118139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wealthy old man is criticized for marrying a woman for he is three times her age. He wittily replies ,\"h, but in 20 years time 2 shall only be twice her age.\" How old is the man and his wife? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86243 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let W represent the wife's present age and M represent the man's present age.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "At the present time the man is 3 times as old as his wife. So 3 times the wife's age equals the<BR>\n" );
document.write( "man's age. In equation form this is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "3W = M<BR>\n" );
document.write( ".<BR>\n" );
document.write( "20 years from now the wife will be W + 20 years old and the man will be M + 20 years old.<BR>\n" );
document.write( "You are told that at that time the man's age will equal twice that of his wife's age. In<BR>\n" );
document.write( "equation form this is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2(W + 20) = M + 20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the left side of this second equation and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2W + 40 = M + 20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Get rid of the 40 on the left side by subtracting 40 from both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2W  = M - 20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And get rid of the M on the right side by subtracting M from both sides. When you do that<BR>\n" );
document.write( "subtraction the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2W - M = -20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But the very first equation told us that M = 3W. So in this latest equation we can substitute<BR>\n" );
document.write( "3W for M to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2W - 3W = -20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Do the subtraction on the left side. 2W minus 3W equals -W so the equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-W = -20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply both sides of this equation by -1 and it becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "W = 20<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since W is the wife's current age, we know that at this time the wife is 20 years old.<BR>\n" );
document.write( "And since the man is presently 3 times as old as his wife, he has to be 60.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "As a check, if the wife is currently 20, in 20 years from now she will be 40. And since<BR>\n" );
document.write( "the man is currently 60 years old, in 20 years he will be 80. At that time will he be<BR>\n" );
document.write( "twice as old as his wife ... is 80 twice as old as 40? Yes it is, so the answers check.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The wife is now 20 and her husband is 60.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem and how to solve it.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Have a happy new year!<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );