Investment A clothing company borrows $700,000. Some of the money is borrowed at 8%, some at 9%, and some at 10% simple annual interest. How much is borrowed at each rate when the total annual interest is $60,500 and the amount borrowed at 8% is three times the amount borrowed at 10%?

amount invested at 10% --- x

amount invested at 8% ---- 3x
amount invested at 9% ----- 700,000-x-3x = 700,000-4x

.1x + .08(3x) + .09(700000-4x) = 60500
times 100
10x + 8(3x) + 9(700000-4x) = 6050000
34x + 6300000 - 36x = 6050000
-2x = -250,000
x = 125,000

amount borrowed at 10% = $125,000
amount borrowed at 8% = 375,000
amount borrowed at 9% = 200,000

To solve this problem, let's break it down into smaller steps.

Step 1: Assign variables to the unknowns in the problem.
Let's assume the amount borrowed at 8% is "x," the amount borrowed at 9% is "y," and the amount borrowed at 10% is "z."

Step 2: Write down the equations based on the given information.
- The total amount borrowed is $700,000, so we have the equation:
x + y + z = 700,000

- The total annual interest obtained from the loans is $60,500, so we have the equation:
0.08x + 0.09y + 0.10z = 60,500

- The amount borrowed at 8% is three times the amount borrowed at 10%, so we have the equation:
x = 3z

Step 3: Solve the equations.
We can use substitution or elimination to solve the system of equations. Here's how:

Substitute x = 3z into the first equation:
3z + y + z = 700,000
4z + y = 700,000 --(Equation 1)

Substitute x = 3z into the second equation:
0.08(3z) + 0.09y + 0.10z = 60,500
0.24z + 0.09y + 0.10z = 60,500
0.34z + 0.09y = 60,500 --(Equation 2)

Now we have a system of equations with two variables (z and y). We can solve for these variables using various methods such as substitution or elimination.

Step 4: Solve the system of equations.
Using the above two equations, you can use substitution or elimination to solve for "z" and "y."

Once you find the values of z and y, you can substitute them back into the values of x.

In this case, the exact values of z, y, and x cannot be determined without more information or constraints. You may need additional information to find unique values for z, y, and x.