document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79810>Question 79810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If y varies directly with x, and y = 280 when x = 400, find the constant of variation k.\r<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 #57281 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=57281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since y varies directly with x, you can write the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k%2Ax ALIGN=MIDDLE  ALT=\"y+=+k%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this equation the k is the constant of variation.<BR>\n" );
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document.write( "The problem then tells you that y = 280 when x is equal to 400.  Substitute these two<BR>\n" );
document.write( "values into your equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k%2Ax ALIGN=MIDDLE  ALT=\"y+=+k%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=280+=+k%2A400 ALIGN=MIDDLE  ALT=\"280+=+k%2A400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can solve for k by dividing both sides by 400 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=280%2F400+=+k ALIGN=MIDDLE  ALT=\"280%2F400+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side can be reduced by dividing both the numerator and denominator by their<BR>\n" );
document.write( "common factor of 40 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+280%2F400+=+%287%2A40%29%2F%2810%2A40%29+=+%287%2Across%2840%29%29%2F%2810%2Across%2840%29%29=+7%2F10+=+0.7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer for k.  If you substitute that value for k into your equation, the<BR>\n" );
document.write( "equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0.7%2Ax ALIGN=MIDDLE  ALT=\"y+=+0.7%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the \"constant of variation\" (sometimes also called<BR>\n" );
document.write( "the \"constant of proportionality\").  <BR>\n" );
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document.write( "This problem involves \"varying directly as ...\" and this means that the equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k%2Ax ALIGN=MIDDLE  ALT=\"y+=+k%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that as x gets bigger, y gets bigger also.  That's why they are said to vary<BR>\n" );
document.write( "\"directly\".<BR>\n" );
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document.write( "Other problems may ask you to find the \"constant of variation\" for quantities that<BR>\n" );
document.write( "vary inversely as ...<BR>\n" );
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document.write( "For problems involving \"inversely as ...\" the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k%2A%281%2Fx%29+=+k%2Fx ALIGN=MIDDLE  ALT=\"y+=+k%2A%281%2Fx%29+=+k%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can then solve for k by substituting the given corresponding values of y and x, almost<BR>\n" );
document.write( "the same as above.  For example, if your original problem had told you that y varied<BR>\n" );
document.write( "inversely as x and that when y = 280 then x = 400, you could find k by the following<BR>\n" );
document.write( "steps:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k%2Fx ALIGN=MIDDLE  ALT=\"y+=+k%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=280+=+k%2F400 ALIGN=MIDDLE  ALT=\"280+=+k%2F400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply both sides by 400 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=280%2A400+=+k%2A400%2F400 ALIGN=MIDDLE  ALT=\"280%2A400+=+k%2A400%2F400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=112000+=+k ALIGN=MIDDLE  ALT=\"112000+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the equation would become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+112000%2Fx ALIGN=MIDDLE  ALT=\"y+=+112000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that as x gets bigger, y gets smaller ... and that's why the two have a relationship<BR>\n" );
document.write( "that varies \"inversely\". </SPAN>\n" );
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