document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935621>Question 935621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solving it.i tried it again and again but still not getting it.  some amount out of $7000 was lent at 6% p.a. and the remaining was lent at 4%p.a.<BR>\n" );
document.write( "if the total simple interest in 5 years was $1600, find the amount lent 6% p.a </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568862 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=568862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x equal the amount invested at 6%.<BR>\n" );
document.write( "let y equal the amount invested at 4%.\r<BR>\n" );
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document.write( "total amount invested is 7000, so x + y = 7000\r<BR>\n" );
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document.write( "simple interest formula is:\r<BR>\n" );
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document.write( "i = n * r * p\r<BR>\n" );
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document.write( "i = total interest<BR>\n" );
document.write( "n = number of years<BR>\n" );
document.write( "r = annual rate of interest<BR>\n" );
document.write( "p = principal\r<BR>\n" );
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document.write( "x is the principal that is invested at 6%.<BR>\n" );
document.write( "y is the principal that is invested at 4%.\r<BR>\n" );
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document.write( "total interest is 1600, so 5 * .06 * x + 5 * .04 * y = 1600\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 + y = 7000<BR>\n" );
document.write( "5 * .06 * x + 5 * .04 * y = 1600\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( "5 * .06 * x + 5 * .04 * y = 1600 becomes:<BR>\n" );
document.write( ".3 * x + .2 * y = 1600\r<BR>\n" );
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document.write( "your 2 equations now are:\r<BR>\n" );
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document.write( "x + y = 7000<BR>\n" );
document.write( ".3 * x + .2 * y = 1600\r<BR>\n" );
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document.write( "solve for y in the first equation to get y = 7000 - x.\r<BR>\n" );
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document.write( "substitute 7000 - x for y in the second equation to get:\r<BR>\n" );
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document.write( ".3 * x + .2 * (7000 - x) = 1600\r<BR>\n" );
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document.write( "solve for x in this equation:\r<BR>\n" );
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document.write( "start with:<BR>\n" );
document.write( ".3 * x + .2 * (7000 - x) = 1600<BR>\n" );
document.write( "distribute the multiplication to get:<BR>\n" );
document.write( ".3 * x + .2 * 7000 - .2 * x = 1600<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( ".3 * x + 1400 - .2 * x = 1600 <BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( ".1 * x + 1400 = 1600<BR>\n" );
document.write( "subtract 1400 from both sides of the equation to get:<BR>\n" );
document.write( ".1 * x = 200<BR>\n" );
document.write( "divide both sides of the equation by .1 to get:<BR>\n" );
document.write( "x = 2000\r<BR>\n" );
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document.write( "since x + y = 7000, and x = 2000, then y must be equal to 5000.\r<BR>\n" );
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document.write( "x + y = 7000 becomes 2000 + 5000 = 7000 which becomes 7000 = 7000 which is good.\r<BR>\n" );
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document.write( "5 * .06 * x + 5 * .04 * y = 1600 becomes .3 * 2000 + .2 * 5000 = 1600 which becomes 600 + 1000 = 1600 which becomes 1600 = 1600 which is also good.\r<BR>\n" );
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document.write( "the solution looks good and your answer is that the amount lent at 6% per year is equal to 2000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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