document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320305>Question 320305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate? Answer by checkley77\r<BR>\n" );
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document.write( "In this solution, where does the -1000 come from in the last line before \"proof\"<BR>\n" );
document.write( ".04X+.0225(33,000-X)=970<BR>\n" );
document.write( ".04X+742.5-.0225X=970<BR>\n" );
document.write( ".0175X=970-742.5<BR>\n" );
document.write( ".0175X=227.5<BR>\n" );
document.write( "X=227.5/.0175<BR>\n" );
document.write( "X=13,000 INVESTED @ 4%.<BR>\n" );
document.write( "33,000-1,000=20,000 INVESTED @ 2.25%.<BR>\n" );
document.write( "PROOF:<BR>\n" );
document.write( ".04*13,000+.0225*20,000=970<BR>\n" );
document.write( "52O+450=970<BR>\n" );
document.write( "970=970<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 #229424 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=229424\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x return 4% and let y return 2.25%.\r<BR>\n" );
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document.write( "Total money invested is $33,000\r<BR>\n" );
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document.write( "Total interest earned is $970.\r<BR>\n" );
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document.write( "You get:\r<BR>\n" );
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document.write( "x + y = $33,000 (total money)\r<BR>\n" );
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document.write( "and you get:\r<BR>\n" );
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document.write( ".04*x + .0225*y = 970 (total interest)\r<BR>\n" );
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document.write( "You need to solve these 2 equations simultaneously.\r<BR>\n" );
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document.write( "Take the first equation and solve for x or y.\r<BR>\n" );
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document.write( "Solving for y, you get y = 33000 - x.\r<BR>\n" );
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document.write( "Substitute for y in the second equation to get:\r<BR>\n" );
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document.write( ".04 * x + .0225 * (33000 - x) = 970\r<BR>\n" );
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document.write( "You have now reduced the number of unknowns in the equation to 1 which can be solved.\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( ".04 * x + .0225 * 33000 - .0225 * x = 970\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( ".0175 * x + .0225 * 33000 = 970\r<BR>\n" );
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document.write( "Simplify further to get:\r<BR>\n" );
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document.write( ".0175 * x + 742.5 = 970\r<BR>\n" );
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document.write( "Subtract 742.5 from both sides of the equation to get:\r<BR>\n" );
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document.write( ".0175 * x = 227.5\r<BR>\n" );
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document.write( "Divide both sides of the equation by .0175 to get:\r<BR>\n" );
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document.write( "x = 13000\r<BR>\n" );
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document.write( "Since x + y = 33000, that means that y must be equal to 33000 - 13000 which makes y equal to 20000.\r<BR>\n" );
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document.write( "You have x = 13000 and y = 20000 which makes x + y = 33000\r<BR>\n" );
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document.write( "You have .04*x + .0225 * y becomes .04 * 13000 + .0175 * 20000 which becomes 520 + 450 which makes .04*x + .0225 * y = 970.\r<BR>\n" );
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document.write( "Both equations check out with the values of x = 13000 and y = 20000 so you're good.\r<BR>\n" );
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document.write( "That $33,000 minus $1,000 must have been a typo.\r<BR>\n" );
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document.write( "It was supposed to be $33,000 - $13,000.\r<BR>\n" );
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