document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152349>Question 1152349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A woman has a total of $12,000 to invest. She invests part of the money in an account that pays 6% per year and the rest in an account that pays 8% per year. If the interest earned in the first year is $820, how much did she invest in each account?\r<BR>\n" );
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document.write( "She invested $     at 6% and $    at 8%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774375 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=774375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If an algebraic solution is required, then the solution provided by the other tutor is a good presentation of the usual method for solving the problem.<br><BR>\n" );
document.write( "This kind of problem -- as well as a great deal of similar types of problems -- is very common on competitive middle school or high school math contests.  Here is a quick way to solve this kind of problem with a few quick calculations -- much faster than with the equation used in the formal algebraic method.<br><BR>\n" );
document.write( "(1) Find out how the actual interest of $820 compares to the interest that would have been earned if the whole amount were invested at each of the two rates:<BR>\n" );
document.write( "$12,000 at 6% --> $720 interest<BR>\n" );
document.write( "actual -- $820 interest<BR>\n" );
document.write( "$12,000 at 8% --> $960 interest<br><BR>\n" );
document.write( "From $720 to $960 is a difference of $240; from $720 to $820 is a difference of $100.  So the actual interest is \"100/240 = 5/12 of the way\" from $720 to $960.<br><BR>\n" );
document.write( "Since the actual interest if 5/12 of the way from the amount it would have been if all the money had been invested at 6% to the amount it would have been if it had all been invested at 8%, that means 5/12 of the total was invested at 8%.<br><BR>\n" );
document.write( "ANSWER: 5/12 of the $12,000, or $5000, at 8%; the other $7000 at 6%.<br><BR>\n" );
document.write( "CHECK: .08(5000)+.06(7000) = 400+420 =820<br><BR>\n" );
document.write( "All the words of explanation might make this seem like a lengthy process; but it is not.  Being good with mental arithmetic, I solve this kind of problem typically in 7-8 seconds once I have read the given information.<br><BR>\n" );
document.write( "Without all the words, here are the needed calculations:<BR>\n" );
document.write( ".06(12000) = 720; .08(12000) = 960<BR>\n" );
document.write( "960-720 = 240; 820-720 = 100; 100/240 = 5/12<BR>\n" );
document.write( "(5/12)*12000 = 5000<br><BR>\n" );
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