Answer
The amount at $7\%=\$1500$.
The amount at $9\%=\$4500$.
Work Step by Step
Step 1:- Assume unknown quantities as variables.
Let the amount at $7\%$ $=x$.
Let the amount at $9\%$ $=y$.
Step 2:- Write system of equations.
The given values are
Total amount $= \$6000$
Total interest $= \$510$
Or we can write.
$\Rightarrow x+y=6000$ ...... (1)
$\Rightarrow 0.07x+0.09y=510$ ...... (2)
Step 3:- Solve the system of equations.
Multiply equation (1) by $-0.07$.
$\Rightarrow -0.07x-0.07y=-420$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 0.07x+0.09y-0.07x-0.07y=510-420$
Simplify.
$\Rightarrow 0.02y=90$
Divide both sides by $0.02$.
$\Rightarrow \frac{0.02y}{0.02}=\frac{90}{0.02}$
Simplify.
$\Rightarrow y=4500$
Plug the value of $y$ into equation (1).
$\Rightarrow x+4500=6000$
Isolate $x$.
$\Rightarrow x=6000-4500$
Simplify.
$\Rightarrow x=1500$.
Step 4:- Check the answers.
Substitute the values of $x$ and $y$ into equation (2).
$\Rightarrow 0.07(1500)+0.09(4500)=510$
$\Rightarrow 105+405=510$
$\Rightarrow 510=510$. True.
