document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=217489>Question 217489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A palindrome is a number that reads the same forwards and backwards. The sum of a particular set of three consecutive positive integers is a three-digit palindrome. If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164098 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=164098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  palindrome is a number that reads the same forwards and backwards.<BR>\n" );
document.write( " The sum of a particular set of three consecutive positive integers is a three-digit palindrome. <BR>\n" );
document.write( "If the sum is less than 220, what is the greatest possible value for the largest of the three integers in the set?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Less than 220 therefore the number is 212 or the 1st and 3rd digit = 1<BR>\n" );
document.write( "I tried 212, does not have an integer solution.\r<BR>\n" );
document.write( "\n" );
document.write( "Let the 1st and 3rd digit = 1<BR>\n" );
document.write( "Let the middle digit = x<BR>\n" );
document.write( "Let consecutive integers = y, y+1, y+2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "y + (y+1) + (y+2) = 100 + 10x + 1<BR>\n" );
document.write( ";<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "3y + 3 = 10x + 101<BR>\n" );
document.write( ";<BR>\n" );
document.write( "3y = 10x + 101 - 3<BR>\n" );
document.write( ";<BR>\n" );
document.write( "3y = 10x + 98<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x%2B98%29%2F3 ALIGN=MIDDLE  ALT=\"%2810x%2B98%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find a value for x that will give an integer value for y<BR>\n" );
document.write( "The sum of the numerator has to be a multiply of 3<BR>\n" );
document.write( "x = 7<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%287%29%2B98%29%2F3 ALIGN=MIDDLE  ALT=\"%2810%287%29%2B98%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28168%29%2F3 ALIGN=MIDDLE  ALT=\"%28168%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 56<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Try this<BR>\n" );
document.write( "56 + 57 + 58 = 171, satisfies the problem </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );