document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204027>Question 1204027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the ages of a daughter and mother is 56 years; after four years the age of the mother will be three times that of the daughter. What is the age of the daughter and the mother, respectively? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840023 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let's look at two different ways to set the problem up using a single variable.  We could use two variables; but the work required to reach the answer is usually easier if we use a single variable.<br><BR>\n" );
document.write( "Probably the standard approach...<br><BR>\n" );
document.write( "let x = daughter's age<BR>\n" );
document.write( "then 56-x = mother's age (the sum of their ages is 56)<br><BR>\n" );
document.write( "x+4 = daughter's age in 4 years<BR>\n" );
document.write( "(56-x)+4 = 60-x = mother's age in 4 years<br><BR>\n" );
document.write( "In 4 years, the mother's age will be 3 times the daughter's age:<br><BR>\n" );
document.write( "60-x = 3(x+4)<BR>\n" );
document.write( "60-x = 3x+12<BR>\n" );
document.write( "48 = 4x<BR>\n" );
document.write( "x = 12<br><BR>\n" );
document.write( "ANSWERS: The daughter's age is x=12; the mother's age is 56-x = 44<br><BR>\n" );
document.write( "A different possible setup....<br><BR>\n" );
document.write( "let x = daughter's age in 4 years<BR>\n" );
document.write( "then 3x = mother's age in 4 years<br><BR>\n" );
document.write( "The sum of their ages in 4 years will be 56+4+4 = 64:<br><BR>\n" );
document.write( "x+3x = 64<BR>\n" );
document.write( "4x = 64<BR>\n" );
document.write( "x = 16<br><BR>\n" );
document.write( "ANSWERS: the daughter's age is x-4 = 16-4 = 12; the mother's age now is 3x-4 = 48-4 = 44<br><BR>\n" );
document.write( "Note that the algebra needed to solve the problem is easier with this alternative setup....<br><BR>\n" );
document.write( "The lesson is that you should always be open to the possibility of setting up a problem in different ways.<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );