document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622619>Question 622619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as much in the lower-yielding account because it is less risky. His annual interest is $4,180. How much did he invest 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 #391597 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=391597\">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 6% simple interest.<BR>\n" );
document.write( "Let y be the amount of money invested at 10% simple interest.<BR>\n" );
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document.write( "Express the interest rates in decimal form: 6% = 0.06 and 10% = 0.10<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 0.06x.<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 0.10*y.<BR>\n" );
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document.write( "Now we need to write two equations using the information in the problem to model the situation. <BR>\n" );
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document.write( "The man puts twice as much in the lower-yielding account because it is less risky. In other words,<BR>\n" );
document.write( "[the amount invested at 6%] = [2] * [amount invested at 10%]<BR>\n" );
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document.write( "In algebra, we can write this relationship as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The amount the man earns in interest is $4,180. In other words,<BR>\n" );
document.write( "[interest earned at 6%] + [interest earned at 10%] = [$4,180]<BR>\n" );
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document.write( "In algebra, we can write<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06x%2B0.10y=4180 ALIGN=MIDDLE  ALT=\"0.06x%2B0.10y=4180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We have a system of two equations and two variables. We will use the substitution method to solve for x and y. The first equation states that x=2y, so we substitute 2y for x in the second equation.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06x%2B0.10y=4180 ALIGN=MIDDLE  ALT=\"0.06x%2B0.10y=4180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.06%282y%29%2B0.10y=4180 ALIGN=MIDDLE  ALT=\"0.06%282y%29%2B0.10y=4180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.12y%2B0.10y=4180 ALIGN=MIDDLE  ALT=\"0.12y%2B0.10y=4180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.22y=4180 ALIGN=MIDDLE  ALT=\"0.22y=4180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of the equation by 0.22<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=19000 ALIGN=MIDDLE  ALT=\"y=19000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In the context of this problem, y=19000 means that the man invested $19,000 in the account earning 10% simple interest. Since he invested twice as much in the account eating 6%, he must have invested $38,000 at 6%.<BR>\n" );
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document.write( "The final step is to check that this allocation of the money actually earns $4,180 in total interest.<BR>\n" );
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document.write( "$38,000 at 6% interest earns $2,280 since 0.06*38000=2280<BR>\n" );
document.write( "$19,000 invested at 10% interest earns $1,900 since 0.10*19000=1900<BR>\n" );
document.write( "$2,280+1,900 is $4,180 so everything checks out.<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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