<PRE><B>Question 1136546</B>
&lt;br&gt;
(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.&lt;br&gt;
(2) Find the income from the 13% investment:&lt;br&gt;
{{{0.13(3700) = 481}}}&lt;br&gt;
$481 of the total income was from the investment at 13%.&lt;br&gt;
(3) Determine the combined income from the 6% and 10% investments:&lt;br&gt;
{{{787-481 = 306}}}&lt;br&gt;
The total income from the 6% and 10% investments was $306.&lt;br&gt;
(4) Now here is a completely different method for determining how the $3500 was split between the 6% and 10% investments.&lt;br&gt;
All $3500 at 6% would produce income of $210; all at 10% would produce income of $350.&lt;br&gt;
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.&lt;br&gt;
350-210 = 140; 306-210 = 96; 96/140 = 24/35.&lt;br&gt;
$306 is 24/35 of the way from $210 to $350; this means 24/35 of the $3500 was invested at the higher rate.&lt;br&gt;
24/35 of $3500 = $2400 at 10%; the rest, $1100, at 6%.&lt;br&gt;
ANSWERS: $3700 at 13%; $2400 at 10%; $1100 at 6%.</PRE>