document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059554>Question 1059554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ages of Sam, Tontom, and Ramon are consecutive integers. Sam is younger then Ramon but older than Tonton. Sam's mother is thrice as old as Sam and 14 years older than twice as old as Ramon. Find the ages of each. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674585 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=674585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let:<BR>\n" );
document.write( "   S = Sam's age<BR>\n" );
document.write( "   T = Tonton's age<BR>\n" );
document.write( "   R = Ramon's age<BR>\n" );
document.write( "—<BR>\n" );
document.write( "  S<R  and  S>T   (given)<BR>\n" );
document.write( "   This info implies  T<S<R so:\r<BR>\n" );
document.write( "\n" );
document.write( "   T=youngest age<BR>\n" );
document.write( "   S=T+1<BR>\n" );
document.write( "   R=T+2<BR>\n" );
document.write( "—<BR>\n" );
document.write( "Let M = mother's age<BR>\n" );
document.write( "    M = 3(T+1)    (\"Thrice as old as Sam.\"  Recall S=T+1)<BR>\n" );
document.write( "    M = 2(T+2)+14  (\"14 yrs older than twice as old as Ramon.\"  Recall R=T+2)<BR>\n" );
document.write( "—<BR>\n" );
document.write( "Now we can solve for T (2 eqns, 2 unknowns).  M is easily eliminated from the above two eqns by setting the two right hand sides equal to each other:\r<BR>\n" );
document.write( "\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%28T%2B1%29+=+2%28T%2B2%29%2B14++ ALIGN=MIDDLE  ALT=\"+3%28T%2B1%29+=+2%28T%2B2%29%2B14++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve for T:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3T+%2B+3+=+%282T%2B4%29+%2B+14+ ALIGN=MIDDLE  ALT=\"+3T+%2B+3+=+%282T%2B4%29+%2B+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+T+=+15+ ALIGN=MIDDLE  ALT=\"+T+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "—\r<BR>\n" );
document.write( "\n" );
document.write( "Answer:<BR>\n" );
document.write( "   Tonton is 15<BR>\n" );
document.write( "   Sam is 16<BR>\n" );
document.write( "   Ramon is 17   \r<BR>\n" );
document.write( "\n" );
document.write( "—\r<BR>\n" );
document.write( "\n" );
document.write( "Check (using the age relations of Sam's mother):<BR>\n" );
document.write( "   3*16 = 48 <BR>\n" );
document.write( "    14+2*17 = 14+34 = 48   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );