document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011904>Question 1011904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x varies inversely as y and x = 2 when y = 8, find x when y = 4. PLEASE HELP <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627716 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=627716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> direct variation is y = kx\r<BR>\n" );
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document.write( "inverse variation is y = k/x\r<BR>\n" );
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document.write( "k is called the constnat of variation.\r<BR>\n" );
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document.write( "it is always the same for the particular variation problem you are trying to solve.\r<BR>\n" );
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document.write( "with direct variation, solve for k to get k = y/x.\r<BR>\n" );
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document.write( "with inverse variation, solve for k to get k = yx.\r<BR>\n" );
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document.write( "first you solve for k.\r<BR>\n" );
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document.write( "then you use k to solve for y or x.\r<BR>\n" );
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document.write( "in your problem, you are dealing with inverse variation.\r<BR>\n" );
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document.write( "the formula to use is y = k/x.\r<BR>\n" );
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document.write( "solve for k to get k = xy.\r<BR>\n" );
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document.write( "when x = 2 and y = 8, k = xy becomes k = 2*8 which becomes k = 16.\r<BR>\n" );
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document.write( "now, when x = 4, the formula of y = k/x becomes y = 16/x which becomes y = 16/4.\r<BR>\n" );
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document.write( "solve for y to get y = 16/4 = 4\r<BR>\n" );
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document.write( "when x = 4, y = 4.\r<BR>\n" );
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document.write( "when x = 2, y = 8<BR>\n" );
document.write( "when x = 4, y = 4\r<BR>\n" );
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document.write( "what happened?\r<BR>\n" );
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document.write( "first of all, your constant of variation is always the same after you solve for it initially.\r<BR>\n" );
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document.write( "2 * 8 = 16<BR>\n" );
document.write( "4 * 4 = 16\r<BR>\n" );
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document.write( "second of all:\r<BR>\n" );
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document.write( "when x = 2, y = 8<BR>\n" );
document.write( "when x = 4, y = 4\r<BR>\n" );
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document.write( "you multiplied x by 2 and you divided y by 2.\r<BR>\n" );
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document.write( "that's an inverse relationship.\r<BR>\n" );
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document.write( "if you multiply x by 2 and you multiply y by 2, that's a direct relationship.<BR>\n" );
document.write( "if you multiply x by 2 and you divide y by 2, that's an inverse relationship.\r<BR>\n" );
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document.write( "let's look at the same problem one more time, this time we'll do both direct and inverse.\r<BR>\n" );
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document.write( "you are given when x = 2, y = 8\r<BR>\n" );
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document.write( "solve for direct relationship:\r<BR>\n" );
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document.write( "direct relationship formula is y = kx.<BR>\n" );
document.write( "solve for k to get k = y/x which is equal to 8/2 which is equal to 4.<BR>\n" );
document.write( "when x = 4, y = kx becomes y = 4*4 which becomes y = 16.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "when x = 2, y = 8<BR>\n" );
document.write( "when x = 4, y = 16<BR>\n" );
document.write( "y is always 4 * x because the constant of variation is 4.<BR>\n" );
document.write( "k is always equal to y/x and is always equal to 4.<BR>\n" );
document.write( "8/2 = 4<BR>\n" );
document.write( "16/4 = 4<BR>\n" );
document.write( "in this example, when you multiplied 2 by 2 to get 4 then you multiplied 8 by 2 to get 16.<BR>\n" );
document.write( "that's a direct relationship.\r<BR>\n" );
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document.write( "solve for inverse relationship:\r<BR>\n" );
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document.write( "inverse relationship formula is y = k/x.<BR>\n" );
document.write( "solve for k to get k = xy which is equal to 2*8 which is equal to 16.<BR>\n" );
document.write( "when x = 4, y = k/x becomes y = 16/4 which becomes y = 4.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "when x = 2, y = 8<BR>\n" );
document.write( "when x = 4, y = 4<BR>\n" );
document.write( "y is always 16/x because the constant of variation is 16.<BR>\n" );
document.write( "k is always equal to xy and is always equal to 16.<BR>\n" );
document.write( "2*8 = 16<BR>\n" );
document.write( "4*4 = 16<BR>\n" );
document.write( "in this examle, when you multiplied 2 by 2 to get 4, then you divided 8 by 2 to get 4.<BR>\n" );
document.write( "that's an inverse relationship.\r<BR>\n" );
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document.write( "here's a reference on the constant of variation you might find helpful.\r<BR>\n" );
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document.write( "here's some references on variation you might find useful.\r<BR>\n" );
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