document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70101>Question 70101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve the following word problem:\r<BR>\n" );
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document.write( "Bob invested $20,000, part at 14% and part at 13%.  If the total interest at the end of the year is $2,720, how much did he invest at 14%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49979 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=49979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Bob invested $20,000, part at 14% and part at 13%.  If the total interest at the end of <BR>\n" );
document.write( "the year is $2,720, how much did he invest at 14%?\r<BR>\n" );
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document.write( "It takes two equations to solve this equation.  But before beginning, let's define F as the<BR>\n" );
document.write( "amount of money invested at 14% and T as the amount invested at 13%.<BR>\n" );
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document.write( "Since the total amount of money invested is $20,000 we can add F and T and set that sum<BR>\n" );
document.write( "equal to the $20,000.  In equation form this first one of two our equations becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+%2B+T+=+20000 ALIGN=MIDDLE  ALT=\"F+%2B+T+=+20000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The problem tells you the interest Bob makes on the amount F is 14% of F.  You can write <BR>\n" );
document.write( "this as:<BR>\n" );
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document.write( "Interest on F = 0.14*F<BR>\n" );
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document.write( "Similarly the interest Bob makes on the amount T is 13% of T.  You can write this as:<BR>\n" );
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document.write( "Interest on T = 0.13*T.<BR>\n" );
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document.write( "These two amounts of interest have to add up to be the total annual interest of $2,720<BR>\n" );
document.write( "In equation form this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.14F+%2B+0.13T+=+2720 ALIGN=MIDDLE  ALT=\"0.14F+%2B+0.13T+=+2720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is the second of the equations that you can use to solve this problem.\r<BR>\n" );
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document.write( "There are several ways that you could solve this system of two equations.  Let's use the<BR>\n" );
document.write( "substitution method.  Return to the first equation and see that it can be solved for F<BR>\n" );
document.write( "by subtracting T from both sides. If you do that subtraction you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+F+=+20000+-+T ALIGN=MIDDLE  ALT=\"+F+=+20000+-+T\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now substitute that value for F into your second equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.14%2820000-T%29+%2B+0.13T+=+2720 ALIGN=MIDDLE  ALT=\"0.14%2820000-T%29+%2B+0.13T+=+2720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying out the first term on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2800+-+0.14T+%2B+0.13T+=+2720 ALIGN=MIDDLE  ALT=\"2800+-+0.14T+%2B+0.13T+=+2720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms containing T.  That sum is -0.01T and it replaces the two terms,<BR>\n" );
document.write( "resulting in the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2800+-+0.01T+=+2720 ALIGN=MIDDLE  ALT=\"2800+-+0.01T+=+2720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now subtract 2800 from both sides to eliminate the 2800 on the left side.  When you subtract<BR>\n" );
document.write( "it from the right side (2720 - 2800) the result is -80.  Therefore, the equation is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.01T+=+-80 ALIGN=MIDDLE  ALT=\"-0.01T+=+-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply both sides by -1 to eliminate the negative signs and get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.01T+=+80 ALIGN=MIDDLE  ALT=\"0.01T+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally divide both sides by 0.01 (or you can multiply both sides by 100 also) and 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=T+=+8000 ALIGN=MIDDLE  ALT=\"T+=+8000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since you now know that T = $8,000 and the total amount invested is $20,000 you also know<BR>\n" );
document.write( "that the amount invested at 14% (F) has to be $12,000.  So the answer you were looking for<BR>\n" );
document.write( "is $12,000.\r<BR>\n" );
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document.write( "Let's check it:\r<BR>\n" );
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document.write( "Do F and T add up to be $20,000?<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8000+%2B+12000+=+20%2C000 ALIGN=MIDDLE  ALT=\"8000+%2B+12000+=+20%2C000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That works.  Then does 14% of F and 13% of T add up to be $2720?<BR>\n" );
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document.write( "0.14*(12000) + 0.13(8000) = 2720}}}<BR>\n" );
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document.write( "Do the multiplications on the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1680+%2B+1040+=+2720 ALIGN=MIDDLE  ALT=\"1680+%2B+1040+=+2720\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side does add up to equal the right side, so this works also.  The problem is <BR>\n" );
document.write( "correct and you know that the answer of $12,000 is correct for the amount invested <BR>\n" );
document.write( "at 14%.<BR>\n" );
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document.write( "Hope that this helps you understand the problem a little better, and aids you in figuring<BR>\n" );
document.write( "out when you are given two different limits on the problem (in this case the limits of<BR>\n" );
document.write( "the total amount of interest and the total amount invested) that you are likely going to<BR>\n" );
document.write( "need to solve two equations to get the answer.  </SPAN>\n" );
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