Answer
The amount invested at a rate of $5\%$ is $\$20,000$ and the amount invested at a rate of $7\%$ is $\$60,000$.
Work Step by Step
Let the amount invested at a rate of $5\%$ be x.
$\begin{align}
& {{I}_{5}}=\frac{PR}{100} \\
& =\frac{5x}{100}
\end{align}$
Now, the amount invested at a rate of $7\%$ is $80,000-x$. Therefore,
${{I}_{7}}=\frac{\left( 80,000-x \right)7}{100}$
Therefore, the total interest earned is
$\begin{align}
& {{I}_{5}}+{{I}_{7}}=5200 \\
& \frac{5x}{100}+\frac{\left( 80,000-x \right)7}{100}=5200 \\
& \frac{280,000-x}{50}=5200 \\
& x=20,000
\end{align}$
Thus, the amount invested at a rate of $5\%$ is $\$20,000$ and the amount invested at a rate of $7\%$ is $\$80,000-\$20,000=\$60,000$.
