document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=433642>Question 433642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) A garrison has enough food to last for 24 days. How much longer will the food last if each individual ration can be reduced by 20 %?<BR>\n" );
document.write( "b) By how much will each individual  ration have to be reduced if the food is to last 40 days? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #300603 by </B><A HREF=/tutors/aboutme.mpl?userid=rwm><B>rwm(914)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rwm><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=300603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let F = the number of pounds in the total food supply.<BR>\n" );
document.write( "The soldiers will use up the food in 24 days.\r<BR>\n" );
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document.write( "(a) Let x = amount of food (in pounds) each soldier eats per day.<BR>\n" );
document.write( "   In 24 days, they will eat 24x pounds of food, using up the F pounds of supply.<BR>\n" );
document.write( "We have:  24x  =  F *\r<BR>\n" );
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document.write( "We reduce each soldier's ration by 20%,<BR>\n" );
document.write( "   then each soldier gets only 80% of his normal amount.<BR>\n" );
document.write( "That is, each soldier eats 0.80x pounds of food per day.<BR>\n" );
document.write( "   And this will last N days.<BR>\n" );
document.write( "We have:  N(0.80x)  =  F **\r<BR>\n" );
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document.write( "Equate the two statements:  N(0.80x)  =  24x\r<BR>\n" );
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document.write( "  Divide by x:  0.80x  =  24\r<BR>\n" );
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document.write( "Divide by 0.80:  x  =  30\r<BR>\n" );
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document.write( "   Therefore, the food will last 30 days, 6 days longer.\r<BR>\n" );
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document.write( "(b) We want the food to last 40 days.\r<BR>\n" );
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document.write( "Each soldier will get a fraction of what he usually gets.<BR>\n" );
document.write( "   Call that fraction r.<BR>\n" );
document.write( "Each soldier gets rx pounds of food per day.<BR>\n" );
document.write( "   In 40 days, they will eat: 40rx pounds of food.<BR>\n" );
document.write( "In part (a), the total amount of food is 24x.\r<BR>\n" );
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document.write( "So we have:  40rx = 24x   ��   r = 24/40 = 3/5  =  60%\r<BR>\n" );
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document.write( "Each soldier will get only 60% of his normal ration.\r<BR>\n" );
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document.write( "Therefore, each ration is reduced by 40%.<BR>\n" );
document.write( " </SPAN>\n" );
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