document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149612>Question 1149612</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Phyllis invested 27000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 1570 dollars. How much money did she invest at each rate? </SPAN>\n" );
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document.write( "By the standard algebraic solution method....<br><BR>\n" );
document.write( "Let x be the amount at 5%; then the amount at 7% is 27000-x.  Then the total interest is 1570 dollars:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%28x%29%2B.07%2827000-x%29+=+1570 ALIGN=MIDDLE  ALT=\".05%28x%29%2B.07%2827000-x%29+=+1570\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05x%2B1890-.07x+=+1570 ALIGN=MIDDLE  ALT=\".05x%2B1890-.07x+=+1570\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...<br><BR>\n" );
document.write( "You can finish the solution by that method.<br><BR>\n" );
document.write( "Here is a non-algebraic method for finding the answer to \"mixture\" problems like this that I find much easier and faster than that algebraic approach.<br><BR>\n" );
document.write( "(1a) $27000 all at 5% would yield $1350 interest<BR>\n" );
document.write( "(1b) the actual interest was $1570<BR>\n" );
document.write( "(1c) $27000 all at 7% would yield $1890 interest<br><BR>\n" );
document.write( "(2) The actual interest of $1570 is 220/540 = 11/27 of the way from $1350 to $1890.  (If it helps, picture the three interest amounts on a number line.  $1350 to $1570 is a difference of $220; $1350 to $1890 is a difference of $540.  So $1570 is 220/540 of the way from $1350 to $1890.)<br><BR>\n" );
document.write( "That means 11/27 of the investment was at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 11/27 of $27,000, or $11,000, at 7%; the other $16,000 at 5%.<br><BR>\n" );
document.write( "CHECK: .07(11000)+.05(16000) = 770+800 = 1570<br><BR>\n" );
document.write( " </SPAN>\n" );
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