document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210597>Question 1210597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Liam and Noah shared a collection of 540 vintage stamps. Liam sold 2/5 fewer stamps than Noah. After the sale, Noah found that the number of stamps he had remaining was exactly 2/3 of the number of stamps he had sold. If Liam’s remaining stamps accounted for 4/7 of the total stamps the two boys possessed at the end, how many stamps did Liam have at first? </SPAN>\n" );
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document.write( "FAULTY DATA!!<br><BR>\n" );
document.write( "Choose a variable:<BR>\n" );
document.write( "x = number Noah sold<br><BR>\n" );
document.write( "The number Noah had left was 2/3 the number he sold:<BR>\n" );
document.write( "(2/3)x = number Noah had left<br><BR>\n" );
document.write( "Liam sold \"2/5 fewer\" than Noah -- i.e., he sold 3/5 AS MANY as Noah:<BR>\n" );
document.write( "(3/5)x = number Liam sold<br><BR>\n" );
document.write( "Then...<br><BR>\n" );
document.write( "x + (3/5)x = (8/5)x = total sold<br><BR>\n" );
document.write( "540-(8/5)x = total remaining<br><BR>\n" );
document.write( "Liam's remaining stamps were 4/7 of the total remaining, so Noah's remaining stamps were 3/7 of the total remaining:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29x=%283%2F7%29%28540-%288%2F5%29x%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29x=%283%2F7%29%28540-%288%2F5%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "multiply by 21 to clear fractions<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x=9%28540-%288%2F5%29x%29 ALIGN=MIDDLE  ALT=\"14x=9%28540-%288%2F5%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x=4860-%2872%2F5%29x ALIGN=MIDDLE  ALT=\"14x=4860-%2872%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70x=24300-72x ALIGN=MIDDLE  ALT=\"70x=24300-72x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=142x=24300 ALIGN=MIDDLE  ALT=\"142x=24300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x = 24300/142 = 171 9/71<br><BR>\n" );
document.write( "Obviously the answer should be a positive integer....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );