document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047698>Question 1047698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose M is jointly proportional to x and y and inversely proportional to the square of z. If x is doubled, y is decupled, and z is tripled, is the value of M changed, and if so, by what factor?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663236 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=663236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> m1 = (x * y) / z^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 = (2 * x * 10 * y) / (3 * z^2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 / m1 = [(2 * x * 10 * y) / (3 * z^2)] / [(x * y) / (z^2)]\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since (a/b) / (c/d) is the same as (a/b) * (d/c), your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 / m1 = (2 * x * 10 * y) / (3 * z^2) * (z^2) / (x * y)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is equivalent to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 / m1 = (2 * x * 10 * y * z^2) / (3 * z^2 * x * y)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the x and the y and the z^2 in the numerator cancel out the x and the y and the z^2 in the denominator and you are left with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 / m1 = (2 * 10) / 3 which is equal to 20/3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by m1 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 = 20 / 3 * m1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this says that m2 is 20/3 times as large as m1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to see if this is correct, just provide random values for x, y, and z, and see if the ratio is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 5<BR>\n" );
document.write( "y = 10<BR>\n" );
document.write( "z = 15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m1 = x * y / z^2 becomes m1 = (5 * 10) / (225) which becomes m1 = 50 / 225\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m2 = (2 * x * 10 * y) / (3 * z^2) becomes m2 = (2 * 5 * 10 * 10) / (3 * 225) which becomes m2 = 1000 / 675.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you take 50 / 225 and multiply it by 20 / 3, you get 1000 / 675.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this confirmed, for me, that the solution is good and that m2 is 20/3 times as large as m1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i believe this is what you're looking for.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );