document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136030>Question 1136030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Phyllis invested 43000dollars, a portion earning a simple interest rate of 5<BR>\n" );
document.write( "percent per year and the rest earning a rate of 7<BR>\n" );
document.write( "percent per year. After one year the total interest earned on these investments was 2430 dollars. How much money did she invest at each rate?\r<BR>\n" );
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document.write( "At rate 5percent : <BR>\n" );
document.write( "At rate 7percent : </SPAN>\n" );
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document.write( "Here is a completely different method without algebra which, if you understand how to use it, can get you to the answer to a problem like this much faster and with far less effort than traditional algebraic methods.<br><BR>\n" );
document.write( "This is essentially a mixture problem -- you are mixing investments at 5% and 7% and receiving an overall percentage return somewhere between 5% and 7%.<br><BR>\n" );
document.write( "The key to this method of solving mixture problems is that the ratio in which the total investment is split exactly determines where the overall percentage lies between the 5% and 7%.<br><BR>\n" );
document.write( "$43,000 all at 5% would yield $2150 interest.<BR>\n" );
document.write( "$43,000 all at 7% would yield $3010 interest.<br><BR>\n" );
document.write( "Find where the actual interest of $2430 lies between $2150 and $3010:<br><BR>\n" );
document.write( "3010-2150 = 860; 2430-2150 = 280; 280/860 = 28/86 = 14/43<br><BR>\n" );
document.write( "Those simple calculations show that $2430 is 14/43 of the way from $2150 to $3010; that means 14/43 of the total investment was at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 14/43 of $43,000, or $14,000, at 7%; the rest, $29,000, at 5%.<br><BR>\n" );
document.write( "CHECK: .07(14000)+.05(29000) = 980+1450 = 1430 </SPAN>\n" );
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