document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197548>Question 1197548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A teacher invests $12,000 in accounts and earns $$870 in interest for the year. Part of the money was invested at 6.38% and the remainder at 7.83%, both simple interest. How much was invested at each rate?<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 #830846 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A setup for a solution by a standard algebraic method....<br><BR>\n" );
document.write( "x = amount invested at 6.38%<BR>\n" );
document.write( "12000-x = amount invested at 7.83%<br><BR>\n" );
document.write( "The total interest was $870:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.0638%28x%29%2B.0783%2812000-x%29=870 ALIGN=MIDDLE  ALT=\".0638%28x%29%2B.0783%2812000-x%29=870\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The solution is straightforward; but the numbers are ugly.  Using a calculator might be a good idea for doing the actual arithmetic.<br><BR>\n" );
document.write( "An informal solution.... The numbers are still ugly; but in the end you get the answer with less work.<br><BR>\n" );
document.write( "(1) Use a calculator to find that $870 interest on $12000 is an interest rate of 7.25%.<BR>\n" );
document.write( "(2) Using a number line and simple arithmetic, determine that 7.25% is 87/145 = 3/5 of the way from 6.38% to 7.83%.<BR>\n" );
document.write( "(3) That means 3/5 of the total was invested at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 3/5 of $12,000, or $7200, at 7.83%; the other $4800 at 6.38%.<br><BR>\n" );
document.write( "CHECK (use a calculator): .0638(4800)+.0783(7200)=870<br><BR>\n" );
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