document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615830>Question 615830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Roberto invested some money at 8%, and then invested $2000 more than twice this amount at 12%. His total annual income from the two investments was $4720. How much was invested at 12%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387328 by </B><A HREF=/tutors/aboutme.mpl?userid=dragonwalker><B>dragonwalker(73)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dragonwalker><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=387328\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us say that the amount invested at 8% is a.\r<BR>\n" );
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document.write( "A percentage simply represents how many units out of 100 so 8% can be written as 8/100 or 0.08 and 12% can therefore be written as 12/100 or 0.12\r<BR>\n" );
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document.write( "so if 'a' is the amount invested at 8% then the amount invested at 12% is:<BR>\n" );
document.write( "2a + 2000<BR>\n" );
document.write( "(twice 'a' plus 2000)\r<BR>\n" );
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document.write( "The gain is the percent of that investment (I assume that it is on the original investment, not accrued).\r<BR>\n" );
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document.write( "So the amount returned from the 8% investment is simply 0.08a\r<BR>\n" );
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document.write( "The amount returned from the 12% investment is 0.12(2a + 2000)\r<BR>\n" );
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document.write( "which can then be simplified by multiplying 0.12 by each part of the formula within the brackets:\r<BR>\n" );
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document.write( "(0.12 x 2a) + (0.12 x 2000) = 0.24a + 240\r<BR>\n" );
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document.write( "So the total return is that money that comes from both investments:<BR>\n" );
document.write( "  = 0.08a + 0.24a + 240<BR>\n" );
document.write( "  = 0.32a + 240\r<BR>\n" );
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document.write( "As we know the amount of the return is $4720 (I assume it represents the interest income)\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "0.32a + 240 = 4720<BR>\n" );
document.write( "0.32a = 4720 - 240<BR>\n" );
document.write( "0.32a = 4480<BR>\n" );
document.write( "so  a = 4480/0.32<BR>\n" );
document.write( "    a = 14000\r<BR>\n" );
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document.write( "So now we know 'a' we can figure out the amount invested at 12 % which is<BR>\n" );
document.write( "2a + 2000\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "2a + 2000 = 2*14000 + 2000<BR>\n" );
document.write( "          = 28000 + 2000<BR>\n" );
document.write( "          = 30000\r<BR>\n" );
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document.write( "The amount invested at 12% is $30000<BR>\n" );
document.write( " </SPAN>\n" );
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