Answer
The fund invested at $5\%$ is $\$6,300$.
and the fund invested at $6\%$ is $\$8,700$.
Work Step by Step
Let the fund invested at $5\%$ be $=x$.
and the fund invested at $6\%$ be $=y$.
Total fund $=\$15,000$.
$\Rightarrow x+y=15,000$...... (1)
Interest from $x$ at $5\%$ $=0.05x$.
Interest from $y$ at $6\%$ $=0.06y$.
Total interest $=\$837$.
$\Rightarrow 0.05x+0.06y=837$......(2)
Multiply equation (1) by $-0.05$.
$\Rightarrow -0.05(x+y)=-0.05(15,000)$
Apply distributive peroperty.
$\Rightarrow -0.05x-0.05y=-750$...... (3)
Add equation (2) and (3).
$\Rightarrow 0.05x+0.06y-0.05x-0.05y=837-750$
Simplify.
$\Rightarrow 0.01y=87 $
Divide both sides by $0.01$.
$\Rightarrow \frac{0.01y}{0.01}=\frac{87}{0.01} $
Simplify.
$\Rightarrow y=8,700$.
Substitute the value of $y$ into equation (1).
$\Rightarrow x+8,700=15,000$
Subtract $8,700$ form both sides.
$\Rightarrow x+8,700-8,700=15,000-8,700$
Simplify.
$\Rightarrow x=6,300$.
