document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697292>Question 697292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chelsea took out three loans for a total of $120,000 to start an organic orchard. Her bank loan was at an interest rate of 8%, the small business loan was at an interest rate of 5% and the mortgage on her house was at an interest rate of 4%. The total simple interest due on the loans in one year was $5750.The annual simple interest on the mortgage was 1600 more than the interest on the bank loan.How much did she borrow from each source?\r<BR>\n" );
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document.write( "Thank you!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430066 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10551)</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=430066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Chelsea took out three loans for a total of $120,000 to start an organic orchard. Her bank loan was at an interest rate of 8%, the small business loan was at an interest rate of 5% and the mortgage on her house was at an interest rate of 4%. The total simple interest due on the loans in one year was $5750.The annual simple interest on the mortgage was 1600 more than the interest on the bank loan.How much did she borrow from each source?\r<BR>\n" );
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document.write( "Let the bank, business, and mortgage loans be D, B, and M, respectively<BR>\n" );
document.write( "Then: D + B + M = 120,000 ------- eq (i)<BR>\n" );
document.write( "Also, .08D + .05B + .04M = 5,750 ----- eq (ii)<BR>\n" );
document.write( "Additionally, .04M = .08D + 1,600 ----- .08D - .04M = - 1,600 ----- eq (iii) <BR>\n" );
document.write( "- .05D - .05B - .05M = - 6,000 ----- Multiplying eq (i) by - .05 ---- eq (iv)\r<BR>\n" );
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document.write( ".03D - .01M = - 250 ---- Adding eqs (ii) & (iv) ------ eq (v) <BR>\n" );
document.write( "- .12D + .04M = 1,000 ----- Multiplying eq (v) by - 4 ---- eq (vi)<BR>\n" );
document.write( ".08D - .04M = - 1,600 ----- eq (iii) <BR>\n" );
document.write( "- .04D = - 600 ------ Adding eqs (iii) & (vi)\r<BR>\n" );
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document.write( "D, or bank loan received = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+600%29%2F-+.04 ALIGN=MIDDLE  ALT=\"%28-+600%29%2F-+.04\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2815000%29 ALIGN=MIDDLE  ALT=\"highlight_green%2815000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ".03(15,000) - .01M = - 250 -------- Substituting 15,000 for D in eq (v)<BR>\n" );
document.write( "450 - .01M = - 250 <BR>\n" );
document.write( "- .01M = - 250 – 450 <BR>\n" );
document.write( "- .01M = - 700\r<BR>\n" );
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document.write( "M, or mortgage loan received = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+700%29%2F-+.01 ALIGN=MIDDLE  ALT=\"%28-+700%29%2F-+.01\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2870000%29 ALIGN=MIDDLE  ALT=\"highlight_green%2870000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "15,000 + B + 70,000 = 120,000 ------- Substituting 15,000 for D, and $70,000 for M in eq (i)<BR>\n" );
document.write( "B + 85,000 = 120,000\r<BR>\n" );
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document.write( "B, or business loan received = 120,000 – 85,000, or $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2835000%29 ALIGN=MIDDLE  ALT=\"highlight_green%2835000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "OR \r<BR>\n" );
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document.write( "If you're familiar with matrices, you can also determine the various loan amounts utilizing that method. \r<BR>\n" );
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document.write( "You can do the check!!\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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