document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151787>Question 1151787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An executive invests $27,000, some at 5% and the rest at 4% annual interest. If he receives an annual return of $1,180, how much is invested at each rate? </SPAN>\n" );
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document.write( "The setup for a traditional algebraic solution, which I will let you finish....<br><BR>\n" );
document.write( "Let x be the amount invested at 5%<BR>\n" );
document.write( "Then (27000-x) is the amount invested at 4%<br><BR>\n" );
document.write( "The total amount of interest is $1180:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.05%28x%29%2B.04%2827000-x%29+=+1180 ALIGN=MIDDLE  ALT=\".05%28x%29%2B.04%2827000-x%29+=+1180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra....<br><BR>\n" );
document.write( "A different solution method, without algebra....<br><BR>\n" );
document.write( "This method, if you understand it, will get you to the answer to this kind of \"mixture\" problem much faster than the algebraic method.<br><BR>\n" );
document.write( "(1) All $27,000 invested at 5% would yield $1350 interest; all invested at 4% would yield $1080 interest.<br><BR>\n" );
document.write( "(2) Look at the three interest amounts -- $1080, $1180, and $1350 -- on a number line.  The actual interest, $1180, is 10/27 of the way from $1080 to $1350. ($1080 to $1350 is a difference of $270; $1080 to $1180 is a difference of $100; $100/$270 = 100/270 = 10/27).<br><BR>\n" );
document.write( "That means 10/27 of the total was invested at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 10/27 of $27,000, or $10,000, at 5%; the other $17,000 at 4%<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( ".04(17000)+.05(10000) = 680+500 = 1180<br><BR>\n" );
document.write( " </SPAN>\n" );
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