document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163312>Question 1163312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sarah is currently four times as old as her daughter Linda.<BR>\n" );
document.write( "in 6 years Sarah will be three time as old as Linda.<BR>\n" );
document.write( "calculate Linda's current age. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787376 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=787376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> s = sarah's age now.<BR>\n" );
document.write( "l = linda's age now.<BR>\n" );
document.write( "sarah is currently 4 times as old as linda.<BR>\n" );
document.write( "that gets you:<BR>\n" );
document.write( "s = 4 * l<BR>\n" );
document.write( "in 6 years, sarah will be 3 times as old as linda.<BR>\n" );
document.write( "that gets you:<BR>\n" );
document.write( "s + 6 = 3 * (l + 6)<BR>\n" );
document.write( "simplify this equation and subtact 6 from both sides to get:<BR>\n" );
document.write( "s = 3 * l + 12<BR>\n" );
document.write( "since s = 4 * l from the first equation, replace s with 4 * l to get:<BR>\n" );
document.write( "4 * l = 3 * l + 12<BR>\n" );
document.write( "solve for l to get:<BR>\n" );
document.write( "l = 12<BR>\n" );
document.write( "s = 4 * l = 48<BR>\n" );
document.write( "in 6 years s is 54 and l is 18.<BR>\n" );
document.write( "at that time, s = 3 * l because 3 * 18 = 54.\r<BR>\n" );
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document.write( "be careful how your word your problem.<BR>\n" );
document.write( "3 times as old is not the same as 3 times older.<BR>\n" );
document.write( "if the current age is 10, then 3 times as old makes the new age equal to 30 which is 20 more than 10 which is 2 times older than 10.<BR>\n" );
document.write( "if the current age is 10, then 3 times older makes the new age equal to 40 which is 30 more than 10 which is 3 times older than 10, but 4 times as old as 10.\r<BR>\n" );
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document.write( "to put it another way:<BR>\n" );
document.write( "y = 3x means y is 3 times as large as x.<BR>\n" );
document.write( "y = 3x + x means y is 3 times larger than x which means that y = 4 times as much as x.\r<BR>\n" );
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document.write( "your problem works with 3 times as much.<BR>\n" );
document.write( "it does not work with 3 times larger because 3 times larger means 4 times as large.<BR>\n" );
document.write( "solve for 3 times larger, you get:<BR>\n" );
document.write( "y = 4x<BR>\n" );
document.write( "y + 6 = 3 * (x + 6) + (x + 6) which becomes y + 6 = 4 * (x + 6) which becomes y + 6 = 4 * x + 24 which becomes y = 4 * x + 18<BR>\n" );
document.write( "y = 4 * x and y = 4 * x + 18 yield two straight line equations that have the same slope, therefore parallel to each other, therefore will never intersect, so there's no way to solve for x.<BR>\n" );
document.write( "on the other hand, y + 6 = 3 * (x + 6) gets you y + 6 = 3 * x + 18 which results in y = 3 * x + 12 and, since y = 4 * l, you get 4 * l = 3 * l + 12 which results in x = 12.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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