document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190918>Question 1190918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reex John’s father is five times older than Reex John and Reex John is twice as old as his sister Princess. In two years, the sum of their ages will be 58. How old is Reex John now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822678 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=822678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem uses language that is bad for mathematics.  The way the problem is written, the ages are all non-integers, which is not valid.<br><BR>\n" );
document.write( "The problem is with the phrase that says the father is \"five times older than\" the son.<br><BR>\n" );
document.write( "In sloppy everyday English, that is nearly always intended to mean the same thing as \"five times as old as\"; but the correct grammatical and mathematical interpretations of the two phrases are different.<br><BR>\n" );
document.write( "If the son's age is x, then \"five times AS OLD AS\" x clearly means 5x.<br><BR>\n" );
document.write( "But if the son's age is x, then \"five times OLDER THAN\" x means x, PLUS 5 more times x, which makes x+5x=6x.<br><BR>\n" );
document.write( "Unfortunately, apparently very few people who write math problems know proper English.  It is nearly always the case that, when an attempt is made to solve a problem like this in which a phrase like \"5 times older than\" is used, the solution turns out to have non-integer values.<br><BR>\n" );
document.write( "So change the statement of the problem to say that Reex John's father is 5 times AS OLD AS Reex John and solve the problem from there.  Since Princess is the youngest...<br><BR>\n" );
document.write( "x = Princess's age<BR>\n" );
document.write( "2x = Reex John's age<BR>\n" );
document.write( "10x = father's age<br><BR>\n" );
document.write( "The sum of the three ages 2 years from now will be 58, so that sum is now 58-6=52.  So<br><BR>\n" );
document.write( "x+2x+10x=52<br><BR>\n" );
document.write( "Solving that give whole number answers for their ages.  I leave it to you to finish<br><BR>\n" );
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