document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277598>Question 277598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was hoping someone could help me with this Question and show me how you put it in an equation. I'm fine until it gets put in a word problem? I'd like to practice to see what I'm doing wrong.<BR>\n" );
document.write( "Thanks!!\r<BR>\n" );
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document.write( "A person invests $36,000, partly at 5%, partly at 6%, and the remainder at 6.5%. The total annual interest is $2,190. Three times the amount invested at 6% equals the amount invested at 5% and 6.5% combined. How much is invested at each rate?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202225 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person invests $36,000, partly at 5%, partly at 6%, and the remainder at 6.5%.<BR>\n" );
document.write( " The total annual interest is $2,190. <BR>\n" );
document.write( "Three times the amount invested at 6% equals the amount invested at 5% and 6.5% combined.<BR>\n" );
document.write( "How much is invested at each rate?<BR>\n" );
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document.write( "Let a = amt at 5%<BR>\n" );
document.write( "Let b = amt at 6%<BR>\n" );
document.write( "let c - amt at 6.5% <BR>\n" );
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document.write( "Write an equation for each statement:<BR>\n" );
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document.write( "\"A person invests $36,000,\"<BR>\n" );
document.write( "a + b + c = 36000 <BR>\n" );
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document.write( "\"The total annual interest is $2,190.\"<BR>\n" );
document.write( ".05a + .06b + .065c = 2190<BR>\n" );
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document.write( "\"Three times the amount invested at 6% equals the amount invested at 5% and 6.5% combined.\"<BR>\n" );
document.write( "3b = a + c<BR>\n" );
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document.write( "How much is invested at each rate?<BR>\n" );
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document.write( "We can replace a + c in the 1st equation with 3b<BR>\n" );
document.write( "3b + b = 36000<BR>\n" );
document.write( "4b = 36000<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36000%2F4 ALIGN=MIDDLE  ALT=\"36000%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = $9000 invested at 6%<BR>\n" );
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document.write( "We know that:<BR>\n" );
document.write( "a + c = 3(9000)<BR>\n" );
document.write( "a + c = 27000<BR>\n" );
document.write( "therefore:<BR>\n" );
document.write( "a = (27000-c)<BR>\n" );
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document.write( "In the 2nd (interest) equation replace a with (27000-c), replace b with 9000, find c<BR>\n" );
document.write( ".05(27000-c) + .06(9000) + .065c = 2190<BR>\n" );
document.write( "1350 - .05c + 540 + .065c = 2190<BR>\n" );
document.write( ".05c + .065c = 2190 - 1350 - 540<BR>\n" );
document.write( ".015c = 300<BR>\n" );
document.write( "c = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F.015 ALIGN=MIDDLE  ALT=\"300%2F.015\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c = $20000 invest at 6.5%<BR>\n" );
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document.write( "I'll let you find the amt invested at 5% (a)<BR>\n" );
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document.write( "Check the total interest then\r<BR>\n" );
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document.write( " </SPAN>\n" );
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