document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124751>Question 124751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this word problem.\r<BR>\n" );
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document.write( "After 8 months of use, the value of Kathy's computer had depreciated to $890.  After 10 months, the value had gone down to $750.  Assume that the value of the computer, V, is a linear function of the number of months of use, t.\r<BR>\n" );
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document.write( "a) Write an equation for the value of the computer after t months of use.<BR>\n" );
document.write( "b) How much did the computer cost originally?<BR>\n" );
document.write( "c) What was the monthly depreciation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91461 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=91461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The present value (V) of the computer is equal to the original cost (C) less the depreciation (D).<BR>\n" );
document.write( "So you can start by writing:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+C-D ALIGN=MIDDLE  ALT=\"V+=+C-D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But, you are to assume that the depreciation (D) is a linear function of (directly proportional to) the number of months of use (t).  So the depreciation (D) can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+kt ALIGN=MIDDLE  ALT=\"D+=+kt\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k is the constant of proportionality. You can find the value of k as follows:<BR>\n" );
document.write( "First, rewrite the equation for the value V in terms of the months of use, t, by replacing D with kt, as:<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+C-kt ALIGN=MIDDLE  ALT=\"V+=+C-kt\"   DISABLED_style= \"max-width:90%; height:auto;\" > You can write two equations, one for each of the given depreciation values and months of use.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D+=+C-kt%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B1%5D+=+C-kt%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D+=+C-kt%5B2%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D+=+C-kt%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute the given values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D+=+890 ALIGN=MIDDLE  ALT=\"V%5B1%5D+=+890\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+8 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D+=+750 ALIGN=MIDDLE  ALT=\"V%5B2%5D+=+750\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+10 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the two equations:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=890+=+C-k%2A%288%29 ALIGN=MIDDLE  ALT=\"890+=+C-k%2A%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite this as:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+890%2B8%2Ak ALIGN=MIDDLE  ALT=\"C+=+890%2B8%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750+=+C-k%2A%2810%29 ALIGN=MIDDLE  ALT=\"750+=+C-k%2A%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite this as:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+750%2B10%2Ak ALIGN=MIDDLE  ALT=\"C+=+750%2B10%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now set these two equations equal to each other to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=890%2B8%2Ak+=+750%2B10%2Ak ALIGN=MIDDLE  ALT=\"890%2B8%2Ak+=+750%2B10%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for k. Subtract 750 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2B8%2Ak+=+10%2Ak ALIGN=MIDDLE  ALT=\"140%2B8%2Ak+=+10%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 8*k from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140+=+2%2Ak ALIGN=MIDDLE  ALT=\"140+=+2%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+70 ALIGN=MIDDLE  ALT=\"k+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) Now you can find the original cost of the computer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+890%2B8%2Ak ALIGN=MIDDLE  ALT=\"C+=+890%2B8%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute k = 70.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+890%2B8%2A70 ALIGN=MIDDLE  ALT=\"C+=+890%2B8%2A70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+890%2B560 ALIGN=MIDDLE  ALT=\"C+=+890%2B560\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+1450 ALIGN=MIDDLE  ALT=\"C+=+1450\"   DISABLED_style= \"max-width:90%; height:auto;\" > or...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+750%2B10%2Ak ALIGN=MIDDLE  ALT=\"C+=+750%2B10%2Ak\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+750%2B10%2A70 ALIGN=MIDDLE  ALT=\"C+=+750%2B10%2A70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+750%2B700 ALIGN=MIDDLE  ALT=\"C+=+750%2B700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+1450 ALIGN=MIDDLE  ALT=\"C+=+1450\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The original cost of the computer is $1,450.00\r<BR>\n" );
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document.write( "The monthly depreciation is just the value, k, or $70.00 per month.<BR>\n" );
document.write( "Or you can calculate it as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C-D%5B1%5D%29%2Ft%5B1%5D+=+%281450-890%29%2F8 ALIGN=MIDDLE  ALT=\"%28C-D%5B1%5D%29%2Ft%5B1%5D+=+%281450-890%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=560%2F8+=+70 ALIGN=MIDDLE  ALT=\"560%2F8+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > or...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C-D%5B2%5D%29%2Ft%5B2%5D+=+%281450-750%29%2F10 ALIGN=MIDDLE  ALT=\"%28C-D%5B2%5D%29%2Ft%5B2%5D+=+%281450-750%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=700%2F10+=+70 ALIGN=MIDDLE  ALT=\"700%2F10+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );