document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636217>Question 636217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> System of linear equations word problem. Help please!\r<BR>\n" );
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document.write( "An Investment of 54,000 was made by a club. It was split into three parts lasting only year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from investments was $4260. The interest from the first was 6 times from the second. Find the amounts of the three parts of the investments.<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 #400856 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=400856\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "System of linear equations word problem. Help please!\r<BR>\n" );
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document.write( "An Investment of 54,000 was made by a club. It was split into three parts lasting only year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from investments was $4260. The interest from the first was 6 times from the second. Find the amounts of the three parts of the investments.\r<BR>\n" );
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document.write( "Let the amounts invested at 8%, 6%, and 9% be E, S, and N, respectively<BR>\n" );
document.write( "Forming equations based on info provided, we have:<BR>\n" );
document.write( "E + S + N = 54,000 ------ eq (i)\r<BR>\n" );
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document.write( ".08E + .06S + .09N = 4,260 <BR>\n" );
document.write( "8E + 6S + 9N = 426,000 ---- Multiplying by 100 ------ eq (ii)\r<BR>\n" );
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document.write( ".08E = 6(.06S) ----- .08E = .36S <BR>\n" );
document.write( "8E = 36S ---- Multiplying by 100 ------ eq (iii)\r<BR>\n" );
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document.write( "36S + 6S + 9N = 426,000 ------ Substituting 36S for 8E in eq (ii)<BR>\n" );
document.write( "42S + 9N = 426,000 ------ eq (iv) \r<BR>\n" );
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document.write( "– 8E – 8S – 8N = - 432,000 ----- Multiplying eq (i) by – 8 ----- eq (v)<BR>\n" );
document.write( "8E + 6S + 9N = 426,000 ----- eq (ii) <BR>\n" );
document.write( "– 2S + N = - 6,000 ----- Adding eqs (v) & (ii) ----- eq (vi)\r<BR>\n" );
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document.write( "42S + 9N = 426,000 ----- eq (iv)<BR>\n" );
document.write( "18S – 9N = 54,000 ------- Multiplying eq (vi) by – 9 ----- eq (vii)<BR>\n" );
document.write( "60S = 480,000 ------ Adding eqs (iv) & (vii)<BR>\n" );
document.write( "S, or amount invested at 6% = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480000%2F60 ALIGN=MIDDLE  ALT=\"480000%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%288000%29 ALIGN=MIDDLE  ALT=\"highlight_green%288000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "8E = 36(8,000) ----- Substituting 8,000 for S in eq (iii)<BR>\n" );
document.write( "8E = 288,000<BR>\n" );
document.write( "E, or amount invested at 8% = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=288000%2F8 ALIGN=MIDDLE  ALT=\"288000%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2836000%29 ALIGN=MIDDLE  ALT=\"highlight_green%2836000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "36,000 + 8,000 + N = 54,000 ----- Substituting 8,000 for S, and 36,000 for E in eq (i)<BR>\n" );
document.write( "44,000 + N = 54,000<BR>\n" );
document.write( "N, or amount invested at 9% = 54,000 – 44,000, or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2810000%29 ALIGN=MIDDLE  ALT=\"highlight_green%2810000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I’m sure you can do your own check!!\r<BR>\n" );
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document.write( "If you know and are more comfortable with matrices, you could also determine the three unknown amounts using this method. \r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com </SPAN>\n" );
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