document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137123>Question 1137123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two bond funds pay interest at rates that differ by 2%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $660. Find the lower rate of interest.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754965 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=754965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the rate of the first bond be equal to x.<BR>\n" );
document.write( "then the rate of the second bond will be equal to x + .02.<BR>\n" );
document.write( "this is because a rate of 2% is equal to .02.\r<BR>\n" );
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document.write( "since the interest on the first bond is 550, then the rate on the first bond must be the lower rate, so the rate on the first bond is x and the rate on the second bond is x + .02.\r<BR>\n" );
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document.write( "interest = interest rate * principal.\r<BR>\n" );
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document.write( "let i = interest and r = interest rate and p = principal and you get i = r * p.\r<BR>\n" );
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document.write( "when i = 550 and r = x, the equation becomes 550 = x * p.\r<BR>\n" );
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document.write( "when i = 660 and r = x + .02, the equation becomes 660 = (x + .02) * p\r<BR>\n" );
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document.write( "in the equation of 550 = x * p, solve for x to get x = 550 / p.\r<BR>\n" );
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document.write( "in the equation of 660 = (x + .02) * p, replace x with 550 / p to get 660 = (550 / p + .02) * p\r<BR>\n" );
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document.write( "simplify this equation to get 660 = 550 / p * p + .02 * p\r<BR>\n" );
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document.write( "simplify further to get 660 = 550 + .02 * p.\r<BR>\n" );
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document.write( "subtract 550 from both sides of this equation to get 110 = .02 * p\r<BR>\n" );
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document.write( "divide both sides of this equation by .02 to get 110 / .02 = p\r<BR>\n" );
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document.write( "solve for p to get p = 5500.\r<BR>\n" );
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document.write( "this means the principal is 5500.\r<BR>\n" );
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document.write( "your original equations are:\r<BR>\n" );
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document.write( "550 = x * p<BR>\n" );
document.write( "660 = (x + .02) * p\r<BR>\n" );
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document.write( "replace p in these equations to get:\r<BR>\n" );
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document.write( "550 = x * 5500<BR>\n" );
document.write( "660 = (x + .02) * 5500\r<BR>\n" );
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document.write( "solve for x in the first equation to get x = 550 / 5500 = .10.\r<BR>\n" );
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document.write( "since x is equal to .10, then x + .02 must be equal to .12.\r<BR>\n" );
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document.write( "the first equation becomes 550 = .10 * 5500 which becomes 550 = 550.\r<BR>\n" );
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document.write( "the second equation becomes 660 = .12 * 5500 which becomes 660 = 660.\r<BR>\n" );
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document.write( "the soluition is confirmed to be good.\r<BR>\n" );
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document.write( "the lower rate of interest is .1 which is equal to 10%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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