Answer
$\$2500$ at $4\%$.
$\$6500$ at $7\%$.
Work Step by Step
Step 1: Assume unknown quantities as variables.
Let the first fund at $4\%$ interest be $=x$.
Let the second fund at $7\%$ interest be $=y$.
Step 2: Write the system of equations.
$4\%$ of the first fund is $0.04x$.
$7\%$ of the second fund is $0.07y$.
The given values are
Total fund $= \$9000$
Total interest earned $=\$555$.
Or we can write.
$\Rightarrow x+y=9000$ ...... (1)
$\Rightarrow 0.04x+0.07y=555$ ...... (2)
Step 3: Solve the system of equations.
Multiply equation (1) by $-0.04$.
$\Rightarrow -0.04x-0.04y=-360$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.04x+0.07y-0.04x-0.04y=555-360$
Simplify.
$\Rightarrow 0.03y=195$
Divide both sides by $0.03$.
$\Rightarrow \frac{0.03y}{0.03}=\frac{195}{0.03}$
Simplify.
$\Rightarrow y=6500$
Plug the value of $y$ into equation (1).
$\Rightarrow x+6500=9000$
Isolate $x$.
$\Rightarrow x=9000-6500$
Simplify.
$\Rightarrow x=2500$.
Step 4: Check the answers.
Substitute the values of $x$ and $y$ into equation (1).
$\Rightarrow 6500+2500=9000$
$\Rightarrow 9000=9000$ True.
