Problem

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 $\$ \square$.

Solution

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 \(\boxed{20000}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8759/

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