I cannot figure a way to do this problem:

An investment of $98,000 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 third 9%. The total interest from the investments was $7560. The interest from the first investment was 3 times the interest from the second. Find the amounts of the three parts of the investment.

let the three investment amounts be E, S, and N

E+S+N=98000

7500=E*.08+S*.06+N*.09
E*.08=3*S*.06

Three equations, three unknowns, I assume you can put the icing on.

I know how to set it up but I cannot get the three solutions right. I solve by addition and what not but cann't ever get the right answer!

To solve this problem, let's assume the amounts of the three parts of the investment are x, y, and z (in thousands of dollars).

First, we know that the total investment is $98,000. So we have the equation: x + y + z = 98.

Next, we are given that the interest from the first investment is 3 times the interest from the second. Let's denote the interest from the first, second, and third investments as I1, I2, and I3 respectively. We have the equation: I1 = 3 * I2.

Since we know that the interest is calculated by multiplying the amount by the interest rate, and the interest rate for the first investment is 8%, we can write I1 as: I1 = 0.08x. Similarly, I2 can be written as: I2 = 0.06y.

Also, we know that the total interest earned from the three investments is $7560. So we have the equation: I1 + I2 + I3 = 7560.

Substituting the expressions for I1 and I2, we get: 0.08x + 0.06y + 0.09z = 7560.

Finally, we have a system of three equations in three variables:

1) x + y + z = 98
2) 0.08x = 3 * 0.06y
3) 0.08x + 0.06y + 0.09z = 7560

To solve this system of equations, we can use the method of substitution or elimination.

Let's start by solving equation 1) for z: z = 98 - x - y.

Now we can substitute this expression for z into equation 3):

0.08x + 0.06y + 0.09(98 - x - y) = 7560.

Simplifying this equation, we get:

0.08x + 0.06y + 8.82 - 0.09x - 0.09y = 7560.

Combining like terms, we have:

-0.01x - 0.03y = -2220.

Multiplying through by -100 to eliminate the decimals, we get:

x + 3y = 222000.

Now we have a system of two equations:

1) x + y + z = 98
2) x + 3y = 222000

To solve this system, we can use the method of substitution or elimination.