document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127007>Question 1127007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An investor placed her money in a venture paying 7% interest. If she had had another $1500, she would have been able to invest her money at 10% and would have gained an additional $255 in annual interest income. How much did she invest? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743412 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the amount she invested at 7%.<BR>\n" );
document.write( "let x + 1500 = the amount she could have invested at 10%.<BR>\n" );
document.write( "let y = the interest earned.\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( ".07 * x = y<BR>\n" );
document.write( ".10 * (x + 1500) = y + 255\r<BR>\n" );
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document.write( "solve both equations for y to get:\r<BR>\n" );
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document.write( ".07 * x = y<BR>\n" );
document.write( ".10 * (x + 1500) - 255 = y\r<BR>\n" );
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document.write( "simplify the second equation and leave the first equation as is to get:\r<BR>\n" );
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document.write( ".07 * x = y<BR>\n" );
document.write( ".10 * x + .10 * 1500 - 255 = y\r<BR>\n" );
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document.write( "simplify the second equation further and leave the first equation as is to get:\r<BR>\n" );
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document.write( ".07 * x = y<BR>\n" );
document.write( ".10 * x - 105 = y\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( ".03 * x - 105 = 0\r<BR>\n" );
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document.write( "add 105 to both sides of this equation to get:\r<BR>\n" );
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document.write( ".03 * x = 105\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 105 /.03 = 3500.\r<BR>\n" );
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document.write( "3500 is the amount invested at 7%.<BR>\n" );
document.write( "3500 + 1500 = 5000 is the amount that could have been invested at 10%, if she had the extra 1500.\r<BR>\n" );
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document.write( ".07 * 3500 = 245<BR>\n" );
document.write( ".10 * 5000 = 500\r<BR>\n" );
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document.write( "500 - 245 = 255\r<BR>\n" );
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document.write( "interest on amount invested at 10% minus interest on amount invested at 7% = 255, as expressed in the problem statement.\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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document.write( "solution is that the amount that she invested at 7% is 3500.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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