Answer
The fund at $6\%=\$2000$.
The fund at $7\%=\$7000$.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the fund at $6\%$ annual interest be $=x$.
Let the fund at $7\%$ annual interest be $=y$.
Step 2:- Write system of equations.
The given values are
Total fund $= \$9000$
Total interest $= \$610$
Interest for the first fund $=0.06x$.
Interest for the second fund $=0.07y$.
In the equation form
$\Rightarrow x+y=9000$ ...... (1)
$\Rightarrow 0.06x+0.07y=610$ ...... (2)
Step 3:- Solve the system of equations.
Multiply equation (1) by $(-0.06)$.
$\Rightarrow (-0.06)x+(-0.06)y=(-0.06)9000$
$\Rightarrow -0.06x-0.06y=-540$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.06x+0.07y-0.06x-0.06y=610-540$
Simplify.
$\Rightarrow 0.01y=70$
Divide both sides by $0.01$.
$\Rightarrow \frac{0.01y}{0.01}=\frac{70}{0.01}$
Simplify.
$\Rightarrow y=7000$
Plug the value of $y$ into equation (1).
$\Rightarrow x+(7000)=9000$
Isolate $x$.
$\Rightarrow x=9000-7000$
Simplify.
$\Rightarrow x=2000$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 0.06(2000)+0.07(7000)=610$
$\Rightarrow 120+490=610$
$\Rightarrow 610=610$. True.
