document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979180>Question 979180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the total number of pairs of (x,y) satisfying the equation 3x+5y=100, x and y are positive integers<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600473 by </B><A HREF=/tutors/aboutme.mpl?userid=anand429><B>anand429(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=anand429><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=anand429><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=600473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3x + 5y =100<BR>\n" );
document.write( "=> y = (100-3x)/5<BR>\n" );
document.write( "Since x and y are both positive integer,<BR>\n" );
document.write( "so x has to lie between 1 and 33 -------------(condition 1)<BR>\n" );
document.write( "Now y is a integer, hence (100-3x) must be a multiple of 5<BR>\n" );
document.write( "For(100-3x) to be a multiple of 5, 3x also has to be multiple of 5<BR>\n" );
document.write( "which is possible only when x is a multiple of 5  -----(condition 2)<BR>\n" );
document.write( "So, possible values of x meeting conditions 1 and 2 are:-<BR>\n" );
document.write( "x= 5,10,15,20,25,30<BR>\n" );
document.write( "Hence , all possible required pairs of x and y are:-<BR>\n" );
document.write( "5,17<BR>\n" );
document.write( "10,14<BR>\n" );
document.write( "15,11<BR>\n" );
document.write( "20,8<BR>\n" );
document.write( "25,5<BR>\n" );
document.write( "30,2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );