document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206123>Question 1206123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Leon bought some apples. He gave 15 of the apples to his friends and threw away 1/4 of them. He was left with 2/3 of the apples. He then packed the remaining apples into 14 boxes. Some boxes contained 6 apples while the rest contained 12.<BR>\n" );
document.write( "(a) How many apples were packed into the 14 boxes?<BR>\n" );
document.write( "(b) How many boxes contained 6 apples? </SPAN>\n" );
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document.write( "Let x be the number of apples he started with.<br><BR>\n" );
document.write( "After he threw away 1/4 of them, the number he had left was (3/4)x.<br><BR>\n" );
document.write( "After giving 15 to his freinds, the number he had left was (3/4)x-15.<br><BR>\n" );
document.write( "The number he had left was 2/3 of the number he started with, (2/3)x.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29x-15=%282%2F3%29x ALIGN=MIDDLE  ALT=\"%283%2F4%29x-15=%282%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29x-%282%2F3%29x=15 ALIGN=MIDDLE  ALT=\"%283%2F4%29x-%282%2F3%29x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F12%29x=15 ALIGN=MIDDLE  ALT=\"%281%2F12%29x=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%2A12=180 ALIGN=MIDDLE  ALT=\"x=15%2A12=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "He started with 180 apples; he finished with (2/3)*180 = 120 apples.<br><BR>\n" );
document.write( "Those 120 apples were packed into 14 boxes, some 6 per box and some 12 per box.<br><BR>\n" );
document.write( "Solving this second part of the problem formally....<br><BR>\n" );
document.write( "x boxes with 6 apples each, plus (14-x) boxes with 12 apples each, totals 120 apples:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28x%29%2B12%2814-x%29=120 ALIGN=MIDDLE  ALT=\"6%28x%29%2B12%2814-x%29=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B168-12x=120 ALIGN=MIDDLE  ALT=\"6x%2B168-12x=120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x=-48 ALIGN=MIDDLE  ALT=\"-6x=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-48%29%2F-6=8 ALIGN=MIDDLE  ALT=\"x=%28-48%29%2F-6=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The number of boxes with 6 apples per box was x=8; the number of boxes with 12 apples each was 14-x = 6.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "(a) 120<BR>\n" );
document.write( "(b) x=8<br><BR>\n" );
document.write( "Solving the second part of the problem mentally, using logical reasoning....<br><BR>\n" );
document.write( "If all 14 boxes contained 6 apples each, the boxes would contain a total of 14*6 = 84 apples.<BR>\n" );
document.write( "But the number of apples in the boxes was 120, which is 120-84 = 36 more.<BR>\n" );
document.write( "Each large box contains 6 more apples than each small box; so the number of large boxes needed for those additional 36 apples is 36/6 = 6.<br><BR>\n" );
document.write( "And again the answer is 6 large boxes and 14-6 = 8 small boxes.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );