document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72373>Question 72373</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! This homework problem I have found to be very difficult, if you could help, that'd be great! I've tried all the ways I can think of to try and come up with even the equation, but haven't been successful.. I think part of my problem was that there aren't any variables.. I tried making up my own, but kept coming up with a different constant each time..\r<BR>\n" );
document.write( "\n" );
document.write( "Grapefruit problem:<BR>\n" );
document.write( "Suppose that you are shopping at a supermarket and find that the Texas grapefruits have twice the diameter of the Florida ones, but cost seven times as much. Recalling that the volumes of similarly shaped solids vary directly with the cube of a linear dimension such as a diameter, you instantly determine which kind of grapefruit gives you more for your money. Which one does, and why?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank-you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51807 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=51807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the diameter of grapefruits of Texas be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5BT%5D ALIGN=MIDDLE  ALT=\"D%5BT%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that of Florida be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5BF%5D ALIGN=MIDDLE  ALT=\"D%5BF%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Let the volume of grapefruits of Texas be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BT%5D ALIGN=MIDDLE  ALT=\"V%5BT%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that of Florida be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BF%5D ALIGN=MIDDLE  ALT=\"V%5BF%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BT%5D+=+k%2AD%5BT%5D%5E3 ALIGN=MIDDLE  ALT=\"V%5BT%5D+=+k%2AD%5BT%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BF%5D+=+k%2AD%5BF%5D%5E3 ALIGN=MIDDLE  ALT=\"V%5BF%5D+=+k%2AD%5BF%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k = constant of proportionality.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BF%5D%2FV%5BT%5D+=+%28k%2AD%5BF%5D%5E3%29%2F%28k%2AD%5BT%5D%5E3%29 ALIGN=MIDDLE  ALT=\"V%5BF%5D%2FV%5BT%5D+=+%28k%2AD%5BF%5D%5E3%29%2F%28k%2AD%5BT%5D%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BF%5D%2FV%5BT%5D+=+D%5BF%5D%5E3%2FD%5BT%5D%5E3 ALIGN=MIDDLE  ALT=\"V%5BF%5D%2FV%5BT%5D+=+D%5BF%5D%5E3%2FD%5BT%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Given, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5BT%5D+=+2D%5BF%5D ALIGN=MIDDLE  ALT=\"D%5BT%5D+=+2D%5BF%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BF%5D%2FV%5BT%5D+=+D%5BF%5D%5E3%2F%282D%5BF%5D%29%5E3+=+1%2F8 ALIGN=MIDDLE  ALT=\"V%5BF%5D%2FV%5BT%5D+=+D%5BF%5D%5E3%2F%282D%5BF%5D%29%5E3+=+1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the cost of each grapefruit of Texas be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5BT%5D ALIGN=MIDDLE  ALT=\"C%5BT%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that of Florida be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5BF%5D ALIGN=MIDDLE  ALT=\"C%5BF%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5BT%5D+=+7C%5BF%5D ALIGN=MIDDLE  ALT=\"C%5BT%5D+=+7C%5BF%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Then cost per unit volume of grapefruit from Texas is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5BT%5D%2FV%5BT%5D ALIGN=MIDDLE  ALT=\"C%5BT%5D%2FV%5BT%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that of grapefruit from Florida is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5BF%5D%2FV%5BF%5D ALIGN=MIDDLE  ALT=\"C%5BF%5D%2FV%5BF%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%5BT%5D%2FV%5BT%5D%29%2F%28C%5BF%5D%2FV%5BF%5D%29+=+%28C%5BT%5D%2FC%5BF%5D%29%28V%5BF%5D%2FV%5BT%5D%29+=+%287%29%281%2F8%29+=+7%2F8+%3C+1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence, it is wiser to buy the grapefruits from Texas. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );