document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108965>Question 1108965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The annual interest on a $19,000 investment exceeds the interest earned on a $5000 investment by $617.  The $19,000 is invested at a 0.3% higher rate of interest than the $5000.  What is the interest rate of each investment? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724013 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the interest rate on the 19000 dollar investment.\r<BR>\n" );
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document.write( "let y = the interest rate on the 5000 dollar investment.\r<BR>\n" );
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document.write( "you get 19000 * x - 5000 * y = 617\r<BR>\n" );
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document.write( "that means that the annual interest on the 19000 dollar investment is 617 dollars higher than the annual interest on the 5000 dollar investment.\r<BR>\n" );
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document.write( "you are given that the interest rate on the 19000 dollar investment is .3% higher than the interest rate on the 5000 dollar investment.\r<BR>\n" );
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document.write( ".3% is equal to .003.\r<BR>\n" );
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document.write( "this results in x = y + .003\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "19000 * x - 5000 * y = 617<BR>\n" );
document.write( "x = y + .003\r<BR>\n" );
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document.write( "replace x in the first equation with the equivalent value of y + .003 from the second equation to get:\r<BR>\n" );
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document.write( "19000 * (y + .003) - 5000 * y = 617\r<BR>\n" );
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document.write( "simplify to get 19000 * y + 57 - 5000 * y = 617.\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "14000 * y + 57 = 617.\r<BR>\n" );
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document.write( "subtract 57 from both sides to get:\r<BR>\n" );
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document.write( "14000 * y = 560.\r<BR>\n" );
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document.write( "solve for y to get y = 560 / 14000 = .04.\r<BR>\n" );
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document.write( "you have y = .04 and x = .043, since x is .003 more than .04.\r<BR>\n" );
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document.write( "go back to your original problem to see if it makes sense when x = .043 and y = .04\r<BR>\n" );
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document.write( "the original problem says that the difference between the interest on the 19000 dollar investment  and the interest on the 5000 dollar investment is 617 dollars.\r<BR>\n" );
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document.write( "the original problem also states that the interest rate on the 19000 dollar investment is .3% higher than the interest rate on the 5000 dollar investment.\r<BR>\n" );
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document.write( "19000 * .043 - 5000 * .04 is equal to 617 dollars, confirming the solution is correct.\r<BR>\n" );
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document.write( "the solution is that the interest rate on the 19000 investment is 4.3% and the interest rate on the 5000 dollar investment is 4.0%.\r<BR>\n" );
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document.write( "note that .3% = .003\r<BR>\n" );
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document.write( "the percent rate divided by 100 equal the rate.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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