document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184067>Question 1184067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A state employees' pension fund invested a total of one million dollars in two accounts that earned 3.5% and 4.5% annual simple interest. At the end of the year, the total interest earned from the two investments was $43,000. How much was invested at each rate?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849882 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem:\r<BR>\n" );
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document.write( "**Let:**\r<BR>\n" );
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document.write( "* 'x' be the amount invested at 3.5% interest.<BR>\n" );
document.write( "* 'y' be the amount invested at 4.5% interest.\r<BR>\n" );
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document.write( "**Set up the equations:**\r<BR>\n" );
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document.write( "* **Equation 1 (Total investment):** x + y = 1,000,000<BR>\n" );
document.write( "* **Equation 2 (Total interest):** 0.035x + 0.045y = 43,000\r<BR>\n" );
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document.write( "**Solve the equations:**\r<BR>\n" );
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document.write( "One way to solve this is using substitution:\r<BR>\n" );
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document.write( "1. **Solve Equation 1 for x:** x = 1,000,000 - y\r<BR>\n" );
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document.write( "2. **Substitute this value of x into Equation 2:**<BR>\n" );
document.write( "   0.035(1,000,000 - y) + 0.045y = 43,000\r<BR>\n" );
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document.write( "3. **Simplify and solve for y:**<BR>\n" );
document.write( "   35,000 - 0.035y + 0.045y = 43,000<BR>\n" );
document.write( "   0.01y = 8,000<BR>\n" );
document.write( "   y = 800,000\r<BR>\n" );
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document.write( "4. **Substitute the value of y back into Equation 1 to find x:**<BR>\n" );
document.write( "   x + 800,000 = 1,000,000<BR>\n" );
document.write( "   x = 200,000\r<BR>\n" );
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document.write( "**Answer:**\r<BR>\n" );
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document.write( "* $200,000 was invested at 3.5% interest.<BR>\n" );
document.write( "* $800,000 was invested at 4.5% interest.<BR>\n" );
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