document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103449>Question 1103449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person, and the third buyer bought 4/5 of what was left and the last 10 lb. How many pounds of potatoes farmer Bill sold? </SPAN>\n" );
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document.write( "You can work this kind of problem either \"forwards\" or \"backwards\".  I have seen many students who have a preference for one method or the other... so let's look at both methods.<br><BR>\n" );
document.write( "1. Working forwards...<br><BR>\n" );
document.write( "He starts with x pounds of potatoes.<BR>\n" );
document.write( "He sells 1/4 of them, leaving him with (3/4)x pounds.<BR>\n" );
document.write( "He then sells 4/9 of what he has left; that means he still has 5/9.  The number of pounds he has left is 5/9 of (3/4)x, or (5/12)x.<BR>\n" );
document.write( "When he sells \"4/5 of what he has left, plus the last 10 pounds\", it means his last sale was 50 pounds.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F12%29x+=+50 ALIGN=MIDDLE  ALT=\"%285%2F12%29x+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+120 ALIGN=MIDDLE  ALT=\"x+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "He started with 120 pounds of potatoes.<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "start: 120 lb<BR>\n" );
document.write( "first sale: 1/4 of 120 = 30; he has 120-30 = 90 lb left<BR>\n" );
document.write( "second sale: 4/9 of 90 = 40; he has 90-40 = 50 lb left<BR>\n" );
document.write( "last sale: 4/5 of 50, plus 10 more = 40+10 = 50; he has none left<br><BR>\n" );
document.write( "2. Working backwards...<br><BR>\n" );
document.write( "Again, the last sale being \"4/5 of what he has left, plus the last 10 pounds\" means his last sale was 50 pounds.<BR>\n" );
document.write( "Before that, on his second sale, he sold 4/9 of what he had at the time, leaving him with 5/9 of what he had before the sale.  So 5/9 of what he had before the sale is 50 pounds, which means before the second sale he had 90 pounds.<BR>\n" );
document.write( "His first sale was 1/4 of what he started with, leaving him with 3/4 of what he started with.  So 90 pounds is 3/4 of what he started with; that means he started with 120 pounds. </SPAN>\n" );
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