<PRE><B>Question 1203977</B>
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The overall percentage change was -562.50/10000 = -.05625 = -5.625%.&lt;br&gt;
Before doing any calculations, note that this percentage is much closer to -7.8% than it is to +6.7%, so by far the larger amount was invested in the account that lost 7.8%.&lt;br&gt;
A solution using the typical formal algebraic method...&lt;br&gt;
x = amount invested in account that gained 6.7%
10000-x = amount invested in account that lost 7.8%&lt;br&gt;
The overall change was a loss of $562.50:&lt;br&gt;
{{{(.067(x))+(.078(10000-x))=-562.5}}}
{{{.067x-780+.078x=-562.5}}}
{{{.145x=217.5}}}
{{{x=217.5/.145=1500}}}&lt;br&gt;
ANSWER: $1500 was invested in the account that gained 6.7%; the other $8500 in the account that lost 7.8%&lt;br&gt;
CHECK: .067(1500)-.078(8500) = 100.50-663 = -562.50&lt;br&gt;
You can also solve any 2-part &quot;mixture&quot; problem like this informally, performing virtually the same calculations but without the formal algebra.&lt;br&gt;
The three percentages in the problem are -7.8, -5.625, and +6.7.&lt;br&gt;
Look at those percentages on a number line and determine that -5.625 is (2.175)/(14.5) = .15 of the way from -7.8 to +6.7.&lt;br&gt;
That means .15 or 15% of the total was invested in the account that gained 6.7%.&lt;br&gt;
ANSWER: 15% of the $10,000, or $1500, was invested in the account that gained 6.7%; the other $8500 was invested in the account that lost 7.8%.&lt;br&gt;
Note that in this problem, since the numbers were &quot;ugly&quot;, the informal method wasn&#39;t much easier than the formal algebraic method.  But with &quot;nice&quot; numbers that are easy to work with mentally, the informal method can get you to the solution with far less effort.&lt;br&gt;
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