document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241447>Question 241447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mardi recieved an inheritance of $70,000. She invested part at 12% and the rest at 9%.  Her total annual income from the investments was $8100.  Find the amount she invested at 12%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176812 by </B><A HREF=/tutors/aboutme.mpl?userid=texttutoring><B>texttutoring(324)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=texttutoring><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=texttutoring><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have two unknowns (the amounts invested at each rate), so you need two equations.\r<BR>\n" );
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document.write( "Step 1: State your unknowns:\r<BR>\n" );
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document.write( "x = amount of $ invested at 12%<BR>\n" );
document.write( "y = amount of $ invested at 9%\r<BR>\n" );
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document.write( "Step 2: Set up your equations:\r<BR>\n" );
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document.write( "Eqn. 1: x+y=70000<BR>\n" );
document.write( "Eqn. 2: 0.09*x + 0.12*y = 8100\r<BR>\n" );
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document.write( "Step 3: Isolate for y in Eqn. 1:\r<BR>\n" );
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document.write( "y = 70000-x\r<BR>\n" );
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document.write( "Step 4: Plug this value for y into Eqn. 2, and then collect terms to isolate for x:\r<BR>\n" );
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document.write( "0.09*x + 0.12*y = 8100<BR>\n" );
document.write( "0.09*x +0.12(70000-x) = 8100<BR>\n" );
document.write( "0.09*x +0.12*70000 – 0.12*x = 8100<BR>\n" );
document.write( "8400 – 0.03x = 8100<BR>\n" );
document.write( "8400 - 8100 – 0.03x = 8100 - 8100<BR>\n" );
document.write( "8400 - 8100 – 0.03x = 0<BR>\n" );
document.write( "300 = 0.03x<BR>\n" );
document.write( "x = 10000\r<BR>\n" );
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document.write( "Step 5: Now substitute this back into Eqn. 1 to find y:\r<BR>\n" );
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document.write( "y = 70000 – x<BR>\n" );
document.write( "y = 70000 – 10000<BR>\n" );
document.write( "y = 60000\r<BR>\n" );
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document.write( "So the two amounts invested are $10000 at 9% and $60000 at 12%. </SPAN>\n" );
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