document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210589>Question 1210589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fruit seller had a collection of apples, pears, and oranges.<BR>\n" );
document.write( "Initially, 1/4 of the fruits were apples.<BR>\n" );
document.write( "He sold 80 apples and 1/3 of the pears.<BR>\n" );
document.write( "After this, he bought more oranges, increasing the number of oranges by 60%.<BR>\n" );
document.write( "At this point, the number of pears he had left was twice the number of apples he had left.<BR>\n" );
document.write( "Finally, he realized that the total number of fruits he had now was exactly 20% more than the total number he started with.<BR>\n" );
document.write( "How many oranges did the fruit seller have at the very beginning?<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 #854132 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13325)</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=854132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem asks for the number of oranges he started with.  So let that be our variable.<br><BR>\n" );
document.write( "x = original number of oranges<br><BR>\n" );
document.write( "We will need another variable.<br><BR>\n" );
document.write( "y = original number of apples<br><BR>\n" );
document.write( "The original number of apples is 1/4 of the total number of fruits, so the total number of fruits is 4y. This gives us<br><BR>\n" );
document.write( "4y-(x+y) = 3y-x = original number of pears<br><BR>\n" );
document.write( "To start, then, we have<br><BR>\n" );
document.write( "apples: y<BR>\n" );
document.write( "pears: 3y-x<BR>\n" );
document.write( "oranges: x<br><BR>\n" );
document.write( "He sells 80 apples and 1/3 of the pears, leaving...<br><BR>\n" );
document.write( "apples: y-80<BR>\n" );
document.write( "pears: (2/3)(3y-x) = 2y-(2/3)x<BR>\n" );
document.write( "oranges: x<br><BR>\n" );
document.write( "He buys more oranges, increasing the number of oranges by 60% -- i.e., multiplying the number of oranges by 160%, or 8/5.<br><BR>\n" );
document.write( "apples: y-80<BR>\n" );
document.write( "pears: (2/3)(3y-x) = 2y-(2/3)x<BR>\n" );
document.write( "oranges: (8/5)x<br><BR>\n" );
document.write( "After doing that, he has twice as many pears as apples<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y-%282%2F3%29x=2%28y-80%29 ALIGN=MIDDLE  ALT=\"2y-%282%2F3%29x=2%28y-80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y-%282%2F3%29x=2y-160 ALIGN=MIDDLE  ALT=\"2y-%282%2F3%29x=2y-160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x=160 ALIGN=MIDDLE  ALT=\"%282%2F3%29x=160\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=240 ALIGN=MIDDLE  ALT=\"x=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That is what the problem asked us to find, so we are done.<br><BR>\n" );
document.write( "ANSWER: x = 240 oranges<br><BR>\n" );
document.write( "Although the problem doesn't require us to do any more work, it is curious to continue to find the original numbers of apples and pears.<br><BR>\n" );
document.write( "The total number of fruits at the end was 20% more than the number at the beginning.<br><BR>\n" );
document.write( "at the beginning: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y ALIGN=MIDDLE  ALT=\"4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "at the end: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-80%29%2B%282y-%282%2F3%29x%29%2B%288%2F5%29x=3y-80-160%2B384=3y%2B144 ALIGN=MIDDLE  ALT=\"%28y-80%29%2B%282y-%282%2F3%29x%29%2B%288%2F5%29x=3y-80-160%2B384=3y%2B144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total number at the end was 20% greater than -- i.e. 6/5 as much -- as at the beginning:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%2B144=%286%2F5%29%284y%29=%2824%2F5%29y ALIGN=MIDDLE  ALT=\"3y%2B144=%286%2F5%29%284y%29=%2824%2F5%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144=%289%2F5%29y ALIGN=MIDDLE  ALT=\"144=%289%2F5%29y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285%2F9%29144=80 ALIGN=MIDDLE  ALT=\"y=%285%2F9%29144=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The fruits he started with:<BR>\n" );
document.write( "apples: y = 80<BR>\n" );
document.write( "pears: 3y-x = 240-240 = 0<BR>\n" );
document.write( "oranges: 240<br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );