document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004262>Question 1004262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eight elves can pack 12 boxes in 30 minutes how long would it take for six elves to pack 24 boxes?\r<BR>\n" );
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document.write( "8 divided by 12 is 1.5 boxes per elf...<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620762 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Eight elves can pack 12 boxes in 30 minutes how long would it take for six elves to pack 24 boxes?\r<BR>\n" );
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document.write( "formula is:\r<BR>\n" );
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document.write( "rate per elf * number of elves * time = quantity\r<BR>\n" );
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document.write( "rate per elf is equal to x, because we don't know what it is.\r<BR>\n" );
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document.write( "number of elves is 8<BR>\n" );
document.write( "time = 30 minutes.<BR>\n" );
document.write( "quantity = 12 boxes.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x * 8 * 30 = 12\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 12 / (8 * 30) = 12 / 240 = 1/20\r<BR>\n" );
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document.write( "this means that each elf can pack 1/20 of a box in 1 minute.\r<BR>\n" );
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document.write( "this means that 8 * 1/20 * 30 = 12\r<BR>\n" );
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document.write( "that's 8 elves packing 1/20 of a box in one minute each and working for 30 minutes will be able to pack 12 boxes.\r<BR>\n" );
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document.write( "evaluate this equation to get 12 = 12.\r<BR>\n" );
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document.write( "this confirms the solution for the rate that each elf works at is good.\r<BR>\n" );
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document.write( "the problem then asks how long would it take for 6 elves to pack 24 boxes.\r<BR>\n" );
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document.write( "the assumption is that they work at the same rate each as they did in the original problem.\r<BR>\n" );
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document.write( "the same formula applies.\r<BR>\n" );
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document.write( "rate per elf * number of elves * time = quantity\r<BR>\n" );
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document.write( "replace this formula with known quantities of each to get:\r<BR>\n" );
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document.write( "1/20 * 6 * time = 24\r<BR>\n" );
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document.write( "solve for time to get:\r<BR>\n" );
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document.write( "time = 24 * 20 / 6 = 80 minutes.\r<BR>\n" );
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document.write( "did we get it right?\r<BR>\n" );
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document.write( "rate per elf * number of elves * minutes = quantity\r<BR>\n" );
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document.write( "1/20 * 6 * 80 = 1/20 * 480 = 24.\r<BR>\n" );
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document.write( "looks like we got it right.\r<BR>\n" );
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document.write( "you might have been able to solve this logically without knowing that formula.\r<BR>\n" );
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document.write( "you know that 8 elves working for 30 minutes can pack 12 boxes.\r<BR>\n" );
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document.write( "divide that by 30 and you get 8 elves working for 1 minute can pack 12/30 boxes.\r<BR>\n" );
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document.write( "divide that by 8 and you get 1 elve working for 1 minute can pack 12 / 30 / 8 boxes.\r<BR>\n" );
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document.write( "take 12 / 30 / 8 and you get 3 / 30 / 2 which becomes 1 / 20.\r<BR>\n" );
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document.write( "that tells you that 1 elve working for 1 minute can pack 1/20 of a box.\r<BR>\n" );
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document.write( "that tells you that 6 elves working for 1 minute can pack 6/20 of a box.\r<BR>\n" );
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document.write( "if you want to know how long it would take those elves to pack 24 boxes, you would have to divide 24 by (6/20) which is the same as 24 * (20/6) which is equal to 4 * 20 which is equal to 80 minutes.\r<BR>\n" );
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document.write( "you get the same answer.\r<BR>\n" );
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document.write( "the formula is just a formal way of representing it.\r<BR>\n" );
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document.write( "rate of each elf * number of elves * number of minutes = number of packed boxes.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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