document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156306>Question 1156306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> $14,700 is invested, part at 3% and the rest at 2%. If the interest earned from the amount invested at 3% exceeds the interest earned from the amount invested at 2% by $359.00, how much is invested at each rate? (Round to two decimal places if necessary.)\r<BR>\n" );
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document.write( "Define variables x and y and set up a system of two linear equations that represents the information given in the problem. </SPAN>\n" );
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document.write( "x = amount (in dollars) invested at 3%<BR>\n" );
document.write( "y = amount (in dollars) invested at 2%<BR>\n" );
document.write( "There is $14700 invested total, so x+y = 14700 which solves to y = 14700-x. We'll use this equation later in a substitution step.\r<BR>\n" );
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document.write( "Through the simple interest formula, i = P*r*t, we can say<BR>\n" );
document.write( "i = P*r*t = x*0.03*1 = 0.03x = amount of annual interest from the 3% account\r<BR>\n" );
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document.write( "and also<BR>\n" );
document.write( "i = P*r*t = y*0.02*1 = 0.02y = amount of annual interest from the 2% account\r<BR>\n" );
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document.write( "We're told that the amount of interest from the 3% account exceeds the other account's interest by $359, so,<BR>\n" );
document.write( "0.03x = 0.02y+359\r<BR>\n" );
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document.write( "0.03x = 0.02y+359<BR>\n" );
document.write( "0.03x = 0.02(14700-x)+359 .... Substitution; plug in y = 14700-x<BR>\n" );
document.write( "0.03x = 0.02(14700)+0.02(-x)+359 ... distribute<BR>\n" );
document.write( "0.03x = 294-0.02x+359<BR>\n" );
document.write( "0.03x = -0.02x+653<BR>\n" );
document.write( "0.03x + 0.02x = 653 ... add 0.02x to both sides<BR>\n" );
document.write( "0.05x = 653<BR>\n" );
document.write( "x = 653/0.05 ..... divide both sides by 0.05<BR>\n" );
document.write( "x = 13060\r<BR>\n" );
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document.write( "Once you've figured out the value of x, you can find the value of y<BR>\n" );
document.write( "y = 14700 - x<BR>\n" );
document.write( "y = 14700 - 13060<BR>\n" );
document.write( "y = 1640\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "<font size=4 color=red>$13,060</font> invested at 3%<BR>\n" );
document.write( "<font size=4 color=red>$1,640</font> invested at 2%\r<BR>\n" );
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