document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110305>Question 1110305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small cube is cut from a large cube. The ratio of the remaining volume to the original volume is 19:27. If the small cube has sides of length 14cm, find the length of the sides of the large cube (before the small cube was removed). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725309 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=725309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the small cube has sides whose length is 14 cm.<BR>\n" );
document.write( "the volume of the small cube is therefore 14^3 = 2744 cubic cm.<BR>\n" );
document.write( "the ratio of the remaining volume to the original volume is 19:27.\r<BR>\n" );
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document.write( "i understand this to mean the volume of the original cube that remains after the volume of the small cube has been removed.\r<BR>\n" );
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document.write( "if you let x equal the original volume, then x - 2744 is the remaining volume after the small cube has been removed.\r<BR>\n" );
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document.write( "the ratio of the remaining volume to the original volume is 19:27.\r<BR>\n" );
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document.write( "this can be written as 19/27.\r<BR>\n" );
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document.write( "you get 19/27 = (x - 2744) / x\r<BR>\n" );
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document.write( "that'a the ratio of the remaining volume to the original volume.\r<BR>\n" );
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document.write( "cross multiply to get 19 * x = 27 * (x - 2744)\r<BR>\n" );
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document.write( "simplify to get 19 * x = 27 * x - 27 * 2744\r<BR>\n" );
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document.write( "subtract 27 * x from both sides of the equation to get 19 * x - 27 * x = -(27 * 2744)\r<BR>\n" );
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document.write( "simplify to get -8 * x = -74088\r<BR>\n" );
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document.write( "divide both sides of the equation by -8 to get x = 9261.\r<BR>\n" );
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document.write( "that would be the original volume of the cube.\r<BR>\n" );
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document.write( "take the cube root of that to get 21.\r<BR>\n" );
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document.write( "that would be the length of the sides of the original cube.\r<BR>\n" );
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document.write( "the volume of the original cube is 21^3 = 9261.\r<BR>\n" );
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document.write( "the small cube is carved out of it, whose volume is 14^3 = 2744.\r<BR>\n" );
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document.write( "the volume that remains is 9261 - 2744 = 6517.\r<BR>\n" );
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document.write( "the ratio of the remaining volume to the original volume is 19/27.\r<BR>\n" );
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document.write( "6517/9261 simplifies to 19/27, confirming the solution is correct.\r<BR>\n" );
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document.write( "this simplification is performed by dividing both numerator and denominator by 343.\r<BR>\n" );
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document.write( "(6517/343) /(9261/343) = 19/27\r<BR>\n" );
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document.write( "your solution is that the length of the sides of the original cube was 21 cm.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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