document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72964>Question 72964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the mass of an object varies jointly within its density and its volume. If 156 grams of iron has a volume of 20 cm^3 and a density of 7.8 gm/cm^3, what is the volume of 312 grams of iron with the same density?\r<BR>\n" );
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document.write( "Answer:(blank)cu.cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52251 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem tells you that the mass (in grams) of a object varies directly (jointly)<BR>\n" );
document.write( " as the volume in cubic cm and the density in grams per cubic cm. In equation form you can <BR>\n" );
document.write( "write this as:<BR>\n" );
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document.write( "M = k*V*D<BR>\n" );
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document.write( "where M is mass, V is volume, D is density and k is a constant of proportionality that we<BR>\n" );
document.write( "will figure out from the info they gave you.  <BR>\n" );
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document.write( "In this problem we are told that a mass of 156 grams results from a volume of 20 cubic cm<BR>\n" );
document.write( "and a density of 7.8 grams per cubic cm. Plug these values into the equation and you get:<BR>\n" );
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document.write( "156 = k*20*7.8<BR>\n" );
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document.write( "When you do the multiplication on the right side you get:<BR>\n" );
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document.write( "156 = 156k<BR>\n" );
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document.write( "Therefore, k is 1 for this situation, and our equation simplifies to just<BR>\n" );
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document.write( "M = V*D<BR>\n" );
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document.write( "Then you are asked that if you had a mass of 312 grams of this material which has the <BR>\n" );
document.write( "same 7.8 grams per cubic cm density, what is the volume?<BR>\n" );
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document.write( "Start with the equation:<BR>\n" );
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document.write( "M = V*D <BR>\n" );
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document.write( "and substitute the given values:<BR>\n" );
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document.write( "312 = V*7.8<BR>\n" );
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document.write( "Divide both sides by 7.8 and you find that<BR>\n" );
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document.write( "312/7.8 = V<BR>\n" );
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document.write( "which, after the division on the left side, simplifies to <BR>\n" );
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document.write( "40 = V<BR>\n" );
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document.write( "and the units for volume are cubic cm.  So the answer to the problem is that the volume<BR>\n" );
document.write( "of the new sample of the material is 40 cubic cm.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. Don't get confused by <BR>\n" );
document.write( "the constant of proportionality.  It's just in there to make both sides of the equation<BR>\n" );
document.write( "equal and when you get to more advanced problems of this type it is likely to be needed. I just<BR>\n" );
document.write( "showed you how it would fit in and how you would determine it so that later on you won't be<BR>\n" );
document.write( "surprised by it. </SPAN>\n" );
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