An investment of $63,000 was made by a business club. The investment was split into three parts and lasted one year. The first part of the investment earned 8% interest, the second 6% and the third 9%. Total interest from the investments was $4950. The interest from the investment was 4 times the interest from the second. Find totals of the three parts of the investment. What is the amount of the first part of the investment?
To solve this problem, we need to set up a system of equations based on the information given.
Let's denote the amounts of the three parts of the investment as follows:
- The first part of the investment: x dollars
- The second part of the investment: y dollars
- The third part of the investment: z dollars
According to the problem, the total investment was $63,000. Therefore, we can write the equation:
x + y + z = 63,000 ----(Equation 1)
Now, let's determine the interest earned from each part of the investment.
The interest earned from the first part is given as 8% of the first part, which is 0.08x dollars.
The interest earned from the second part is given as 6% of the second part, which is 0.06y dollars.
The interest earned from the third part is given as 9% of the third part, which is 0.09z dollars.
According to the problem, the total interest earned from the three parts is $4950. Therefore, we can write the equation:
0.08x + 0.06y + 0.09z = 4950 ----(Equation 2)
Finally, the problem states that the interest earned from the investment is four times the interest earned from the second part. Hence, we can write the equation:
0.08x = 4(0.06y)
0.08x = 0.24y
Now, we have a system of three equations (Equations 1, 2, and 3) that we can solve to find the values of x, y, and z.
To find the solution, you can use substitution, elimination, or other algebraic methods. Once you solve the system of equations and find the values of x, y, and z, you will be able to determine the amount of the first part of the investment.