Larry Mach invested part of the 21,000 from his salary advance at a simple annual interest rate of 6%, and the remainder at a simple annual interest rate of 4% if the total interest he earned during the year on both accounts was of 1060, determine the amount invested at each rate the company must sell how many tons?

Let's assume that Larry Mach invested x amount of dollars at a 6% annual interest rate.
So, the amount he invested at a 4% annual interest rate would be (21,000 - x) dollars.

Now, we'll calculate the interest earned from both accounts.
The interest earned from the amount invested at a 6% annual interest rate would be: 0.06x.
The interest earned from the amount invested at a 4% annual interest rate would be: 0.04(21,000 - x).

According to the given information, the total interest earned was $1060, so we can set up the following equation:

0.06x + 0.04(21,000 - x) = 1060

Now, let's solve this equation to find the value of x:

0.06x + 0.04(21,000) - 0.04x = 1060
0.06x + 840 - 0.04x = 1060
0.02x + 840 = 1060
0.02x = 1060 - 840
0.02x = 220
x = \frac{220}{0.02}

Now, let's calculate the value of x:

x = \frac{220}{0.02} = 11,000

Therefore, Larry Mach invested $11,000 at a 6% annual interest rate, and the remaining amount (21,000 - 11,000 = $10,000) at a 4% annual interest rate.

Answer: Larry Mach invested $11,000 at a 6% annual interest rate and $10,000 at a 4% annual interest rate.