document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183712>Question 1183712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5 years back the ratio of kate and sharon 4:3. In 5 years, the sum of the ages of kate and sharon will be 90.  how old is sharon right now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814153 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=814153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If in 5 years the sum of their ages will be 90, then 5 years ago the sum of their ages was 70.<br><BR>\n" );
document.write( "5 years ago the ratio of their ages was 4:3, so let their ages then be 4x and 3x. Then<br><BR>\n" );
document.write( "4x+3x=70<BR>\n" );
document.write( "7x=70<BR>\n" );
document.write( "x=10<br><BR>\n" );
document.write( "Their ages 5 years ago were 4x=40 and 3x=30.<br><BR>\n" );
document.write( "ANSWER: Sharon's age now is 30+5=35.<br><BR>\n" );
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document.write( "(Corrected note....)<br><BR>\n" );
document.write( "Note the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28setup%29 ALIGN=MIDDLE  ALT=\"cross%28setup%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > METHOD for setting up the problem shown by the other tutor is fine -- although a bit of explanation of HOW to set up that equation would be helpful to a beginning student.  Indeed, if they had bothered to try to solve the equation they show, they would have found that the equation was wrong....<br><BR>\n" );
document.write( "If you are going to use a formal algebraic solution, take the time to clearly define your variables and expressions, before writing an equation -- as tutor @ikleyn shows in her response.  Trying to write the equation without having a clear understanding of the expressions in the equation can easily lead to errors, as the response from the first tutor shows.<br><BR>\n" );
document.write( "The difference between the setups for the two solutions is that the other tutor's method uses x for Sharon's age now.  That has the small advantage of having the answer for \"x\" being the answer to the problem.  But the resulting algebra is more complicated than what is needed for my solution above.<br><BR>\n" );
document.write( "Nearly always, if a problem gives part of the given information in the form of a ratio, the algebra is easier if you use that given ratio directly to set up the problem.  In this problem, the \"algebra\" involved when the problem is set up that way is so basic that it is possible to solve the problem quickly mentally.<br><BR>\n" );
document.write( "It does have the small disadvantage that you have to add 5 to Sharon's age 5 years ago to get her current age....<br><BR>\n" );
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