document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164248>Question 1164248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You invested $5000 between two accounts paying 3% and 7% annual​ interest, respectively.  If the total interest earned for the year was $190 how much was invested at each​ rate of 3% and 7%? </SPAN>\n" );
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document.write( "(1) A typical formal algebraic setup for solving the problem:<br><BR>\n" );
document.write( "x amount at 3%, plus ($5000-x) amount at 7%, yields $190 interest.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.03%28x%29%2B.07%285000-x%29+=+190 ALIGN=MIDDLE  ALT=\".03%28x%29%2B.07%285000-x%29+=+190\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve using basic algebra; I leave that to you.<br><BR>\n" );
document.write( "(2) A quick and easy way to solve any two-part \"mixture\" problem like this, if a formal algebraic solution is not required:<br><BR>\n" );
document.write( "$5000 all invested at 3% would yield $150 interest; all at 7$ would yield $350 interest.<BR>\n" );
document.write( "The actual interest, $190, is 40/200 = 1/5 of the way from $150 to $350.  (If it helps, picture the three dollar amounts 150, 190, and 350 on a number line; 150 to 190 is a difference of 40, 150 to 350 is a difference of 200, so 190 is 40/200 = 1/5 of the distance from 150 to 350.)<BR>\n" );
document.write( "That means 1/5 of the total was invested at the higher rate.<br><BR>\n" );
document.write( "ANSWER: 1/5 of the $5000, or $1000, at 7%; the other $4000 at 3%.<br><BR>\n" );
document.write( "CHECK: .03(4000)+.07(1000) = 120+70 = 190<br><BR>\n" );
document.write( " </SPAN>\n" );
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