document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288546>Question 288546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jed and Sam each have $X to invest. Jed invests part of his money in an investment account at<BR>\n" );
document.write( "the bank at 10% p.a. interest and the rest in shares at 12.5% per annum. At the end of the year<BR>\n" );
document.write( "Jed receives an income of $1625 from his investments. Sam invests twice as much as Jed in<BR>\n" );
document.write( "shares at 12.5% and puts the rest into an investment account at 8% p.a. At the end of the year<BR>\n" );
document.write( "Sam receives an income of $1650 from his investments. How much did each person originally<BR>\n" );
document.write( "have to invest? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209137 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=209137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Jed and Sam each have $X to invest. Jed invests part of his money in an investment account at<BR>\n" );
document.write( "the bank at 10% p.a. interest and the rest in shares at 12.5% per annum. At the end of the year<BR>\n" );
document.write( "Jed receives an income of $1625 from his investments. Sam invests twice as much as Jed in<BR>\n" );
document.write( "shares at 12.5% and puts the rest into an investment account at 8% p.a. At the end of the year<BR>\n" );
document.write( "Sam receives an income of $1650 from his investments. How much did each person originally<BR>\n" );
document.write( "have to invest?\r<BR>\n" );
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document.write( "let Jed invest y amount @ 12.5% \r<BR>\n" );
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document.write( "he will invest x-y at 10%\r<BR>\n" );
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document.write( "12.5/100 y + 10/100(x-y)=1625\r<BR>\n" );
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document.write( "12.5 y + 10(x-y)= 1625*100\r<BR>\n" );
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document.write( "12.5y + 10x -10y = 162500\r<BR>\n" );
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document.write( "2.5y +10x = 162500-------------  1\r<BR>\n" );
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document.write( "Sam invests 2y at 12%\r<BR>\n" );
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document.write( "The rest he invests at 8% ie: x-2y\r<BR>\n" );
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document.write( "12.5/100 *2y + 8/100*(x-2y)=1650\r<BR>\n" );
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document.write( "25y +8(x-2y) = 1650 *100\r<BR>\n" );
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document.write( "25y +8x-16y= 165000-------------2\r<BR>\n" );
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document.write( "2.5y +10x = 162500-------------  1<BR>\n" );
document.write( "9y +8x  = 165000--------------2\r<BR>\n" );
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document.write( "multiply eq 1 by 8 and eq 2 by 10\r<BR>\n" );
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document.write( "20y +80x = 1300000\r<BR>\n" );
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document.write( "90y +80x = 1650000\r<BR>\n" );
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document.write( "-70y=-350000\r<BR>\n" );
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document.write( "y= -350000/-70\r<BR>\n" );
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document.write( "= 5000\r<BR>\n" );
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document.write( "Jed invest $5000 at 12.5%\r<BR>\n" );
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document.write( "plug the value of y in eq. 1 \r<BR>\n" );
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document.write( "x= 15000 the amount invested by Jed at 8%\r<BR>\n" );
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document.write( "Sam ivests 2y at12.5 %  =10000\r<BR>\n" );
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document.write( "Sam invests $15000 at 8% ( plug the value of y in eq 2)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );