document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145651>Question 145651</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help with 2 word problems<BR>\n" );
document.write( "Solve the following applications problems using any method<BR>\n" );
document.write( " A couple working towards retirement made two investments totaling $15,000. In one year, these investments yielded $1432 in simple interest. Part of the money was invested at 9% and the rest at 10% How much was invested at each rate?\r<BR>\n" );
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document.write( "A car travels 300 miles in the same amount of time that a car traveling 5 miles and hour slower travels 275 miles. At what speed (rate) is each car traveling?<BR>\n" );
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document.write( "With both of these I can get so far and I get stuck Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106286 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=106286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Let x = the amount invested at 9% simple interest. Then $15,000-x = the amount invested at 10% simple interest.<BR>\n" );
document.write( "The interest earned on these two amounts can be expressed as, after changing the percentages to their decimal equivalents:<BR>\n" );
document.write( "0.09x is the interest earned at 9%.<BR>\n" );
document.write( "0.1($15,000-x) is the interest earned at 10%<BR>\n" );
document.write( "The sum of these two amounts is $1,432,so we can set up an equation to find x:<BR>\n" );
document.write( "0.09x+0.1($15,000-x) = $1,432 Simplify.<BR>\n" );
document.write( "0.09x+1500-0.1x = 1432 Combine like-terms.<BR>\n" );
document.write( "(0.09x-0.1x)+1500 = 1432<BR>\n" );
document.write( "-0.01x+1500 = 1432 Subtract 1500 from both sides.<BR>\n" );
document.write( "-0.01x = -68 Divide both sides by -0.01<BR>\n" );
document.write( "x = 6800, so...<BR>\n" );
document.write( "$6,800 was invested at 9% simple interest and $15,000-$6,800 = $8,200 was invested at 10% simple interest.<BR>\n" );
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document.write( "2) Use the distance formula: d = rt where d = distance traveled, r = rate of speed, and t = time of travel.<BR>\n" );
document.write( "Car 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+r%5B1%5D%2At ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+r%5B1%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "Car 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+r%5B2%5D%2At ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+r%5B2%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For car 1, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+300 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > and for car 2 substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+r%5B1%5D-5 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+r%5B1%5D-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+275 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The time of travel,t, is the same for both cars, so...<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+300%2Fr%5B1%5D ALIGN=MIDDLE  ALT=\"t+=+300%2Fr%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+275%2F%28r%5B1%5D-5%29 ALIGN=MIDDLE  ALT=\"t+=+275%2F%28r%5B1%5D-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can write...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fr%5B1%5D+=+275%2F%28r%5B1%5D-5%29 ALIGN=MIDDLE  ALT=\"300%2Fr%5B1%5D+=+275%2F%28r%5B1%5D-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%28r%5B1%5D-5%29+=+275%28r%5B1%5D%29 ALIGN=MIDDLE  ALT=\"300%28r%5B1%5D-5%29+=+275%28r%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300r%5B1%5D-1500+=+275r%5B1%5D ALIGN=MIDDLE  ALT=\"300r%5B1%5D-1500+=+275r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1500 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300r%5B1%5D+=+275r%5B1%5D%2B1500 ALIGN=MIDDLE  ALT=\"300r%5B1%5D+=+275r%5B1%5D%2B1500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=275r%5B1%5D ALIGN=MIDDLE  ALT=\"275r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25r%5B1%5D+=+1500 ALIGN=MIDDLE  ALT=\"25r%5B1%5D+=+1500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 25.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+=+60 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first car was traveling at 60mph and the second car was traveling at (60-5) = 55mph.\r<BR>\n" );
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