document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121668>Question 1121668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rosa has a collection of 2000 construction blocks. They measure 2 cm by 5 cm by 4 cm each. Her toy chest has a volume of 50 cm by 24 cm by 75 cm. Is it possible for Rosa to put all her blocks in the toy chest? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737650 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=737650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> she has 2000 construction blocks.<BR>\n" );
document.write( "they measure 2 cm by 5 cm by 4 cm each.<BR>\n" );
document.write( "her toy chest has a volume of 50 cm by 24 cm by 75 cm.\r<BR>\n" );
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document.write( "if you just go by cubic centimeters, then 2000 construction blocks will have a total volume of 2000 * 2 * 5 * 4 = 80,000 cubic centimeters.\r<BR>\n" );
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document.write( "the toy chest has a volume of 50 by 24 by 75 equals 90,000 cubic centimeters.\r<BR>\n" );
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document.write( "if you just go by volume alone, then it looks like the construction blocks will fit into the toy chest.\r<BR>\n" );
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document.write( "however, the shape of the construction blocks matched up against the shape of the toy chest might make it not possible.\r<BR>\n" );
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document.write( "one possible arrangement would be to put the longest side of the clocks along the longest side of the toy chest.\r<BR>\n" );
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document.write( "the longest side of the toy chest is 75 centimeters.<BR>\n" );
document.write( "the longest side of each block is 5 centimeters.\r<BR>\n" );
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document.write( "75 / 5 = 15 block that can be laid alongside the longest side of the toy chest.\r<BR>\n" );
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document.write( "the next longest side of the toy chest is 50 centimeters.<BR>\n" );
document.write( "the next longest side of each block is 4 centimeters.\r<BR>\n" );
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document.write( "50 / 4 = 12 blocks that can be laid alongside the next longest side of the boy chest.\r<BR>\n" );
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document.write( "those 2 dimensions can hold 15 * 12 = 180 blocks.\r<BR>\n" );
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document.write( "the smallest side of the toy chest is 24 centimeters.<BR>\n" );
document.write( "the smallest side of each side is 2 centimeters.\r<BR>\n" );
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document.write( "24 / 2 = 12 blocks that can be laid alongside the smallest side of the toy chest.\r<BR>\n" );
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document.write( "180 * 12 = 2160 blocks.\r<BR>\n" );
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document.write( "it looks like the blocks will fit.\r<BR>\n" );
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document.write( "there is some wasted space, but not enough to prevent all the blocks from being placed in the toy chest.\r<BR>\n" );
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document.write( "they do need to be put in a compatible configuration however.\r<BR>\n" );
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document.write( "there are ways in which they are put in the toy chest where you won't be able to get 2000 of them in.\r<BR>\n" );
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document.write( "i looked at the possible ways and came up with 4 ways they would fit and 2 ways they wouldn't fit.\r<BR>\n" );
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document.write( "how the blocks are place in the toy chest is a definite factors as to whether they will all fit or not.\r<BR>\n" );
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document.write( "if they are not lined up properly, there will be wasted space that can't be filled, resulting in not enough space to fit all the blocks.\r<BR>\n" );
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document.write( "so, the short answer is yes, they will fit.\r<BR>\n" );
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document.write( "the long answer is that it is dependent on how they are placed in the toy chest.\r<BR>\n" );
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document.write( "here's the results of the excel spreadsheet that contained my investigation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/082303.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the configuration on row 6 and row 8 leaves enough wasted space so that not all the blocks will be able to be fit into the toy chest.\r<BR>\n" );
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document.write( "all the others may have some wasted space but not enough to stop all the blocks from being inserted.\r<BR>\n" );
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