document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112210>Question 1112210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man lends a sum of money to his local council and receives $63 interest on the loan <BR>\n" );
document.write( "Each year. When the rate of interest rises by 0.5%, the annual interest raised to $67.50. <BR>\n" );
document.write( "Calvulate the sum of money lent to the council and the new percentage of interest. <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 #727231 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=727231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the amount of money he lends to the council.\r<BR>\n" );
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document.write( "let r be the interest rate of the loan.\r<BR>\n" );
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document.write( "the interest on the loan is 63 per year.\r<BR>\n" );
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document.write( "x * r = 63\r<BR>\n" );
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document.write( "when the interest rate on the loan is increased by .5%, the annual interest is raised to 67.50.\r<BR>\n" );
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document.write( ".5% / 100 is equal to .005.\r<BR>\n" );
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document.write( "x * (r + .005) = 67.5\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( "x * r = 63<BR>\n" );
document.write( "x * (r + .005) = 67.5\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( "x * r = 63<BR>\n" );
document.write( "x * r + .005 * x = 67.5\r<BR>\n" );
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document.write( "since x * r = 63 from the first equation, replace x * r in the second equation by 63 to get:\r<BR>\n" );
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document.write( "second equation becomes:\r<BR>\n" );
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document.write( "63 + .005 * x = 67.5\r<BR>\n" );
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document.write( "subtract 63 from both sides of this equation to get:\r<BR>\n" );
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document.write( ".005 * x = 4.5\r<BR>\n" );
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document.write( "divide both sides of this equation by .005 to get:\r<BR>\n" );
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document.write( "x = 4.5 / .005\r<BR>\n" );
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document.write( "this results in x = 900.\r<BR>\n" );
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document.write( "go back to your original equation and replace x with 900 and solve for r.\r<BR>\n" );
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document.write( "the first original equation is:\r<BR>\n" );
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document.write( "x * r = 63\r<BR>\n" );
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document.write( "replace x with 900 to get:\r<BR>\n" );
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document.write( "900 * r = 63\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "r = 63/900 = .07\r<BR>\n" );
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document.write( "in the second original equation, replace r + .005 with .075\r<BR>\n" );
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document.write( "the first and second original equations now become:\r<BR>\n" );
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document.write( "900 * .07 = 63 becomes 63 = 63, which is true.\r<BR>\n" );
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document.write( "900 * .075 = 67.5 becomes 67.5 = 67.5, which is true.\r<BR>\n" );
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document.write( "both original equations are true when r = .07.\r<BR>\n" );
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document.write( "this confirms the solution is correct, given the original equations are correct.\r<BR>\n" );
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document.write( "interest rate percent is 100 * interest rate.\r<BR>\n" );
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document.write( "conversely, interest rate is interest rate percent / 100.\r<BR>\n" );
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document.write( "you had to work with interest rate, not percent.\r<BR>\n" );
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document.write( "that'w why we used .5%/100 = .005, rather than .5%, in the equations.\r<BR>\n" );
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