Answer
The amount borrowed for the $5.5\%$ is $55000$ dollars and that for the $6\%$ is $35000$ dollars.
Work Step by Step
Step 1. Assume the amount borrowed for the $5.5\%$ is $x$ dollars and that for the $6\%$ is $y$ dollars.
Step 2. Based on the given conditions, we have $\begin{cases} x+y=90,000\\0.055x+0.06y=5125 \end{cases}$
Step 3. Multiple $0.06$ to the first equation take the difference with the second one to get $0.005x=0.06(90000)-5125=275$, thus $x=55000$ and $y=90000-55000=35000$ dollars.
