Answer
The investment in stocks $=\$5,000$.
The investment in the bonds $=\$6,000$
Work Step by Step
Let the investment in stocks is $x$.
and the investment in the bonds is $y$.
The total investment is.
$\Rightarrow x+y=11,000$ ...... (1)
Annual interest from stocks $=5\%$ of $x$.
$=0.05x$.
Annual interest from bonds $=8\%$ of $y$.
$=0.08y$.
The total interest is.
$\Rightarrow 0.05x+0.08y = 730$ ...... (2)
Multiply equation (1) by $-0.05$.
$\Rightarrow -0.05\cdot (x+y)=-0.05\cdot 11,000$
Apply distributive property.
$\Rightarrow -0.05x-0.05y=-550$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.05x+0.08y -0.05x-0.05y= 730-550$
Add like terms.
$\Rightarrow 0.03y =180$
Divide both sides by $0.03$.
$\Rightarrow \frac{0.03y}{0.03} =\frac{180}{0.03}$
Simplify.
$\Rightarrow y =6,000$
Plug the value of $y$ into equation (1).
$\Rightarrow x+6,000=11,000$
Subtract $6,000$ from both sides.
$\Rightarrow x+6,000-6,000=11,000-6,000$
Simplify.
$\Rightarrow x=5,000$
