An investment of $\mathrm{\$}92,000$ was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned $8\mathrm{\%}$ interest, the second $6\mathrm{\%}$, and the third $9\mathrm{\%}$. Total interest from the investments was $\mathrm{\$}7200$. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment.
The first part of the investment was $\mathrm{\$}◻$.
The second part of the investment was $\mathrm{\$}◻$.
The third part of the investment was $\mathrm{\$}◻$.

Step 1 ：Let's denote the amounts of the three parts of the investment as x, y, and z for the first, second, and third part respectively.

Step 2 ：We know that the total investment is $92,000, so we have the equation $x+y+z=92000$.

Step 3 ：The total interest from the investments was $7200, so we have the equation $0.08x+0.06y+0.09z=7200$.

Step 4 ：The interest from the first investment was 4 times the interest from the second, so we have the equation $0.08x=4\ast 0.06y$.

Step 5 ：Solving these three equations, we find that $x=54000$, $y=18000$, and $z=20000$.

Step 6 ：Final Answer: The first part of the investment was $\boxed{{\displaystyle 54000}}$. The second part of the investment was $\boxed{{\displaystyle 18000}}$. The third part of the investment was $\boxed{{\displaystyle 20000}}$.