document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180221>Question 180221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help with this problem.<BR>\n" );
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document.write( "Suppose you have recieved a total of $1,520 a year in interest from three investments. The interest rates for the investments are 5%, 7%, and 8%. The amount is invested at 5% is half of the amount invested at 7%. The amount invested at 7% is $1,500 less than the amount invested at 8% Find the amount of money invested at each rate.<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 #135068 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=135068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you have received a total of $1,520 a year in interest from three investments. The interest rates for the investments are 5%, 7%, and 8%. The amount is invested at 5% is half of the amount invested at 7%. The amount invested at 7% is $1,500 less than the amount invested at 8% Find the amount of money invested at each rate.<BR>\n" );
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document.write( "Let \"x\" be amt invested at 5%<BR>\n" );
document.write( "Let \"y\" be amt. invested at 7%<BR>\n" );
document.write( "Let \"z\" be amt. invested at 8%<BR>\n" );
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document.write( "Interest Equation: 0.05x + 0.07y + 0.08z = 1520<BR>\n" );
document.write( "Quantity Equation: x = (1/2)y<BR>\n" );
document.write( "Quantity Equation: y = z - 1500<BR>\n" );
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document.write( "Write x and z interms of y:<BR>\n" );
document.write( "x = (1/2)y<BR>\n" );
document.write( "z = y + 1500<BR>\n" );
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document.write( "Substitute into the 1st equation to solve for \"y\":<BR>\n" );
document.write( "0.05((1/2)y) + 0.07y + 0.08(y+1500) = 1520\r<BR>\n" );
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document.write( "Multiply thru by 100 to get:<BR>\n" );
document.write( "5(1/2)y + 7y + 8(y + 1500) = 152000\r<BR>\n" );
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document.write( "(5/2)y + 7y + 8y + 12000 = 152000<BR>\n" );
document.write( "(35/2)y = 140000<BR>\n" );
document.write( "y = $8000.00 (amt. invested at 7%)<BR>\n" );
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document.write( "x = (1/2)y = $4000.00 (amt. invested at 5%)<BR>\n" );
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document.write( "z = y + 1500 = $9500 (amt. invested at 8%)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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