A total of 6000 is invested part 8% and the remainder at 13% how much is invested at each rate if the annual interest is 710$
Let x be the amount invested at 8% interest rate.
The amount invested at 13% interest rate is 6000 - x.
The interest earned from the amount invested at 8% is 0.08x.
The interest earned from the amount invested at 13% is 0.13(6000 - x).
The total interest earned is 710.
0.08x + 0.13(6000 - x) = 710
0.08x + 780 - 0.13x = 710
-0.05x = -70
x = 1400
So, 1400 is invested at 8% and 6000 - 1400 = 4600 is invested at 13%. Answer: \boxed{1400, 4600}.