document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548945>Question 548945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To buy both a new car and a new house, Tina sought two loans totalling $191,610. The simple interest rate on the first loan was 6.3%, while the simple interest rate on the second loan was 8.8%. At the end of the first year, Tina paid a combined interest payment of $16,681.66. What were the amounts of the two loans?\r<BR>\n" );
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document.write( "How do I set up and answer  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357322 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for simple interest is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+P%2A%28+1+%2B+t%2Ar+%29+ ALIGN=MIDDLE  ALT=\"+A+=+P%2A%28+1+%2B+t%2Ar+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amount after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > years<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = original amount<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = annual % interest rate<BR>\n" );
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document.write( "Let the equation for the 1st loan be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+=+P%5B1%5D%2A%28+1+%2B+t%2Ar%5B1%5D+%29+ ALIGN=MIDDLE  ALT=\"+A%5B1%5D+=+P%5B1%5D%2A%28+1+%2B+t%2Ar%5B1%5D+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let the equation for the 2nd loan be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B2%5D+=+P%5B2%5D%2A%28+1+%2B+t%2Ar%5B2%5D+%29+ ALIGN=MIDDLE  ALT=\"+A%5B2%5D+=+P%5B2%5D%2A%28+1+%2B+t%2Ar%5B2%5D+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D+=+.063+ ALIGN=MIDDLE  ALT=\"+r%5B1%5D+=+.063+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B2%5D+=+.088+ ALIGN=MIDDLE  ALT=\"+r%5B2%5D+=+.088+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5B1%5D+%2B+P%5B2%5D+=+191610+ ALIGN=MIDDLE  ALT=\"+P%5B1%5D+%2B+P%5B2%5D+=+191610+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "Adding the 2 equations with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1+ ALIGN=MIDDLE  ALT=\"+t+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+%2B+A%5B2%5D+=+P%5B1%5D+%2B+P%5B1%5D%2Ar%5B1%5D+%2B+P%5B2%5D+%2B+P%5B2%5D%2Ar%5B2%5D+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+%2B+A%5B2%5D+=+191610+%2B+.063P%5B1%5D+%2B+.088P%5B2%5D+ ALIGN=MIDDLE  ALT=\"+A%5B1%5D+%2B+A%5B2%5D+=+191610+%2B+.063P%5B1%5D+%2B+.088P%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The combined interest payment is<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.063P%5B1%5D+%2B+.088P%5B2%5D+=+16681.66+ ALIGN=MIDDLE  ALT=\"+.063P%5B1%5D+%2B+.088P%5B2%5D+=+16681.66+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But also<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5B1%5D+%2B+P%5B2%5D+=+191610+ ALIGN=MIDDLE  ALT=\"+P%5B1%5D+%2B+P%5B2%5D+=+191610+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.063+ ALIGN=MIDDLE  ALT=\"+.063+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and subtract (2) from (1)<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.063P%5B1%5D+%2B+.088P%5B2%5D+=+16681.66+ ALIGN=MIDDLE  ALT=\"+.063P%5B1%5D+%2B+.088P%5B2%5D+=+16681.66+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-.063P%5B1%5D+-+.063P%5B2%5D+=+-12071.43+ ALIGN=MIDDLE  ALT=\"-.063P%5B1%5D+-+.063P%5B2%5D+=+-12071.43+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.025P%5B2%5D+=+4610.23+ ALIGN=MIDDLE  ALT=\"+.025P%5B2%5D+=+4610.23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5B2%5D+=+184409.2+ ALIGN=MIDDLE  ALT=\"+P%5B2%5D+=+184409.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, <BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5B1%5D+%2B+184409.2+=+191610+ ALIGN=MIDDLE  ALT=\"+P%5B1%5D+%2B+184409.2+=+191610+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5B1%5D+=+191610+-+184409.2+ ALIGN=MIDDLE  ALT=\"+P%5B1%5D+=+191610+-+184409.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5B1%5D+=+7200.8+ ALIGN=MIDDLE  ALT=\"+P%5B1%5D+=+7200.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The amounts of the loans were:<BR>\n" );
document.write( "$7,200.80 @ 6.3%<BR>\n" );
document.write( "$184,409.20 @ 8.8%<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+=+P%5B1%5D%2A%28+1+%2B+.063+%29+ ALIGN=MIDDLE  ALT=\"+A%5B1%5D+=+P%5B1%5D%2A%28+1+%2B+.063+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B2%5D+=+P%5B2%5D%2A%28+1+%2B+.088+%29+ ALIGN=MIDDLE  ALT=\"+A%5B2%5D+=+P%5B2%5D%2A%28+1+%2B+.088+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+=+7200.8%2A%28+1+%2B+.063+%29+ ALIGN=MIDDLE  ALT=\"+A%5B1%5D+=+7200.8%2A%28+1+%2B+.063+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B2%5D+=+184409.2%2A%28+1+%2B+.088+%29+ ALIGN=MIDDLE  ALT=\"+A%5B2%5D+=+184409.2%2A%28+1+%2B+.088+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+=+7654.45+ ALIGN=MIDDLE  ALT=\"+A%5B1%5D+=+7654.45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B2%5D+=+200637.21+ ALIGN=MIDDLE  ALT=\"+A%5B2%5D+=+200637.21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The combined interest payment should be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5B1%5D+%2B+A%5B2%5D+-+%28P%5B1%5D+%2B+P%5B2%5D+%29%0D%0A%7B%7B%7B7654.45+%2B+200637.21+-+191610+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+208291.66+-+191610+ ALIGN=MIDDLE  ALT=\"+208291.66+-+191610+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16681.66+ ALIGN=MIDDLE  ALT=\"+16681.66+\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is correct\r<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );