document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173499>Question 173499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam buys 3 kinds of fruit for 40 dollars, 10 dollars, and 1 dollar each. He pays 259 dollars for 100 pieces of fruit. How many of the cheapest did he buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128428 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=128428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the quantities of the 3 kinds of fruit<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+c+=+100 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+c+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40a+%2B+10b+%2B+1%2Ac+=+259 ALIGN=MIDDLE  ALT=\"40a+%2B+10b+%2B+1%2Ac+=+259\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Just observing, I see I have 3 unknowns and only 2 <BR>\n" );
document.write( "equations. It looks like I need another equation,<BR>\n" );
document.write( "but I'll try to solve anyway<BR>\n" );
document.write( "Subtract (1) from (2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39a+%2B+9b+=+159 ALIGN=MIDDLE  ALT=\"39a+%2B+9b+=+159\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13a+%2B+3b+=+53 ALIGN=MIDDLE  ALT=\"13a+%2B+3b+=+53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll make a chart and see if I can get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+b+%2B+c+=+100 ALIGN=MIDDLE  ALT=\"a+%2B+b+%2B+c+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "--   a   --   b  --  c   --  13a+3b  --  a+b+c<BR>\n" );
document.write( "----------------------------------------------<BR>\n" );
document.write( "--   4   ---    0   ---   1    ---    53   -----     5<BR>\n" );
document.write( "--   3   --   14/3  (no good, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a whole number)<BR>\n" );
document.write( "--   1   --   40/3  (no good, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a whole number)<BR>\n" );
document.write( "--   2   ---   9  ---  47  ---    53   ---   100<BR>\n" );
document.write( "These are the only values for a,b, and c that work out<BR>\n" );
document.write( "He bought 47 of the cheapest fruit </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );