document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622654>Question 622654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can $60,000 be invested, part at 7% annual simple interest and the remainder at 12% annual simple interest, so that the interest earned by the two accounts will be equal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391564 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "We can use algebra to solve this.<BR>\n" );
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document.write( "Let x be the amount of money invested at 7% simple interest.<BR>\n" );
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document.write( "The money invested in both accounts sums up to $60,000, so the expression 60000-x represents the amount of money invested at 12% simple interest.<BR>\n" );
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document.write( "Now express the interest rates in decimal form: 7% = 0.07 and 12% = 0.12<BR>\n" );
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document.write( "The amount of interest earned on the the first account is the interest rate times the amount invested, or 0.07x.<BR>\n" );
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document.write( "Likewise, the amount of interest earned on the second account is its interest rate times the amount invested, or 0.12*(60000-x).<BR>\n" );
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document.write( "We want the interest earned on the two accounts to be equal, so we write an equation showing the two expressions to be equal.<BR>\n" );
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document.write( "[interest earned at 7%] = [interest earned at 12%]<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7x=0.12%2860000-x%29 ALIGN=MIDDLE  ALT=\"0.7x=0.12%2860000-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now simplify and solve for x.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7x=7200-0.12x ALIGN=MIDDLE  ALT=\"0.7x=7200-0.12x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add 0.12x to both sides of the equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.7x%2B0.12x=7200 ALIGN=MIDDLE  ALT=\"0.7x%2B0.12x=7200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.19x=7200 ALIGN=MIDDLE  ALT=\"0.19x=7200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by 0.19.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7200%2F0.19 ALIGN=MIDDLE  ALT=\"x=7200%2F0.19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=37894.74 ALIGN=MIDDLE  ALT=\"x=37894.74\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the context of our problem x=37894.74 means that $37,894.74 should be invested in the account with 7% interest.<BR>\n" );
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document.write( "The remainder should be invested in the account with 12% interest. Since 60,000-37,894.74= 22,105.26, we should invest $22,105.26 in the second account.<BR>\n" );
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document.write( "The final step is to check that this allocation of the money actually earns the same amount of interest.<BR>\n" );
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document.write( "$37,894.74 at 7% interest earns $2,652.63 since 0.07*37894.74=2652.63<BR>\n" );
document.write( "$22,105.26 invested at 12% interest earns $2,652.63 since 0.12*22105.26=2652.63<BR>\n" );
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document.write( "That's it. Feel free to email if you have questions about any part of this explanation.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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