document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=57088>Question 57088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Helen Weller invested $15,000 in an account that pays 11% simple interest. How much additional money must be invested in an account that pays 14% simple interest so that the average return on the two investments amounts to 12%?<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 #38800 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=38800\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the additional amount to be invested at 14%\r<BR>\n" );
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document.write( "The interest on the initial $15,000 at 11% would be 0.11($15,000)<BR>\n" );
document.write( "The interest on the additional amount, $x at 14% would be 0.14($x)<BR>\n" );
document.write( "The sum of these two amounts of interest should come to 12% of ($15,000 + $x) or 0.12($15,000+$x).  So...putting it all together. you can write:\r<BR>\n" );
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document.write( "0.11($15000) + 0.14($x) = 0.12($15000+$x) Simplify this and solve for x.<BR>\n" );
document.write( "$1650 + 0.14x = 1800 + 0.12x  Subtracting 0.12x from both sides, you get:<BR>\n" );
document.write( "1650 + 0.02($x) = $1800  Subtract $1650 from both sides.<BR>\n" );
document.write( "0.02($x) = $150  Finally, divide both sides by 0.02<BR>\n" );
document.write( "x = $7500\r<BR>\n" );
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document.write( "So Helen Weller should invest an additional $7,500 at 14% interest to obtain an average rate of return of 12% on the entire amount.\r<BR>\n" );
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document.write( "Check: \r<BR>\n" );
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document.write( "11% of $15,000 = 0.11($15,000) = $1,650<BR>\n" );
document.write( "14% of $7,500 = 0.14($7,500) = $1,050<BR>\n" );
document.write( "The sum: $1,650 + $1,050 = $2,700 total interest.\r<BR>\n" );
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document.write( "12% of ($15,000 + $7,500) = 0.12($22,500) = $2,700 </SPAN>\n" );
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