document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918195>Question 918195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you borrowed $112 from your sister and told her that you would pay $8 a week until the loan is paid.  your brother borrowed $165 from your sister and told her he would pay $13.75 a week until the load is paid.\r<BR>\n" );
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document.write( "1.  write a linear equation that represnets the balance of each loan.  identify the slop and y-intercept of each equation and explain what they represent in the real-life situation.<BR>\n" );
document.write( "2.  use a graph to determine who will pay off their loan first.  explain reasoning.<BR>\n" );
document.write( "3.  explain how you can verify your answer to part (b) algebraically.<BR>\n" );
document.write( "4.  explain the meaning of the intersection of the two lines in terms of the real-life situation.<BR>\n" );
document.write( "5.  after the third week, you decide to pay your sister $11 a week until the load is paid off.  does this change your answer to part 2.  explain reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556949 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the unpaid balance of each loan ( amount still owed )<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of the week after the<BR>\n" );
document.write( "loan is made ( which is week <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Your equation:<BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-8x+%2B+112+ ALIGN=MIDDLE  ALT=\"+y+=+-8x+%2B+112+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your brother's equation:<BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-13.75x+%2B+165+ ALIGN=MIDDLE  ALT=\"+y+=+-13.75x+%2B+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "(1)<BR>\n" );
document.write( "y-intercept occur where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-8%2A0+%2B+112+ ALIGN=MIDDLE  ALT=\"+y+=+-8%2A0+%2B+112+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%280%29+=+112+ ALIGN=MIDDLE  ALT=\"+y%280%29+=+112+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-13.75%2A0+%2B+165+ ALIGN=MIDDLE  ALT=\"+y+=+-13.75%2A0+%2B+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+165+ ALIGN=MIDDLE  ALT=\"+y+=+165+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercepts are the amount of each loan<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "Here's the plots for each loan:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+15%2C+-10%2C+200%2C+-8x+%2B+112%2C+-13.75x+%2B+165+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+15%2C+-10%2C+200%2C+-8x+%2B+112%2C+-13.75x+%2B+165+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The loans are paid off when each line hits the x-axis and<BR>\n" );
document.write( "y-axis ( unpaid balance ) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "You can just set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which<BR>\n" );
document.write( "is the week number when it will be paid<BR>\n" );
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document.write( "(4) <BR>\n" );
document.write( "The intersection is the week number when both owe your<BR>\n" );
document.write( "sister the same amount<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "(5)<BR>\n" );
document.write( "The loan gets paid off sooner, because the equation then <BR>\n" );
document.write( "has a steeper slope and reaches the x-axis ( zero unpaid balance )<BR>\n" );
document.write( "sooner<BR>\n" );
document.write( "------------- \r<BR>\n" );
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document.write( " </SPAN>\n" );
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