An investment of $\$ 92,000$ 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 $8 \%$ interest, the second $6 \%$, and the third $9 \%$. Total interest from the investments was $\$ 7200$. 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 $\$ \square$.
The second part of the investment was $\$ \square$.
The third part of the investment was $\$ \square$.
Answer
Final Answer: The first part of the investment was \(\boxed{54000}\). The second part of the investment was \(\boxed{18000}\). The third part of the investment was \(\boxed{20000}\).
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 \(0.08x = 4 * 0.06y\).
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 \(\boxed{54000}\). The second part of the investment was \(\boxed{18000}\). The third part of the investment was \(\boxed{20000}\).
