document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136546>Question 1136546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person invested ​$7200 for 1​ year, part at 6​%, part at 10​%, and the remainder at 13​%.<BR>\n" );
document.write( "The total annual income from these investments was ​$787. <BR>\n" );
document.write( "The amount of money invested at 13​% was ​$200 more than the amounts invested at 6​% <BR>\n" );
document.write( "and 10​% combined. Find the amount invested at each rate.\r<BR>\n" );
document.write( "\n" );
document.write( "The person invested $​[    ] at 6​%,<BR>\n" );
document.write( "$[    ] at 10​%, and $​[    ] at 13​%. </SPAN>\n" );
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document.write( "(1) Use logical reasoning and simple mental arithmetic, or formal algebra, to determine from the given information that $3700 was invested at 13% and $3500 was split between the 6% and 10% investments.<br><BR>\n" );
document.write( "(2) Find the income from the 13% investment:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.13%283700%29+=+481 ALIGN=MIDDLE  ALT=\"0.13%283700%29+=+481\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "$481 of the total income was from the investment at 13%.<br><BR>\n" );
document.write( "(3) Determine the combined income from the 6% and 10% investments:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=787-481+=+306 ALIGN=MIDDLE  ALT=\"787-481+=+306\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total income from the 6% and 10% investments was $306.<br><BR>\n" );
document.write( "(4) Now here is a completely different method for determining how the $3500 was split between the 6% and 10% investments.<br><BR>\n" );
document.write( "All $3500 at 6% would produce income of $210; all at 10% would produce income of $350.<br><BR>\n" );
document.write( "The ratio in which the $3500 is split between the 6% and 10% investments is exactly determined by where the actual income lies between $210 and $350.<br><BR>\n" );
document.write( "350-210 = 140; 306-210 = 96; 96/140 = 24/35.<br><BR>\n" );
document.write( "$306 is 24/35 of the way from $210 to $350; this means 24/35 of the $3500 was invested at the higher rate.<br><BR>\n" );
document.write( "24/35 of $3500 = $2400 at 10%; the rest, $1100, at 6%.<br><BR>\n" );
document.write( "ANSWERS: $3700 at 13%; $2400 at 10%; $1100 at 6%. </SPAN>\n" );
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