Answer

 I₁= 43000 x I ( the annual interest of 43000$ )

I₂= 37000 ( I- 5%) = 37000 ( 0,95 I ) ( the annual interest of 37000$ )

I₁ + I₂ = 4750 ( the total interest of the year for both amount (43000$ and 37000$)

By placing the value of I₁ and I₂ in the equation of the total year interest:

43000 I + 35150 I = 4750

78150 I = 4750

I = 4750 / 78150 = 6.078% ( we have obtained the annual rate percentage for both amount)

Now to find the annual interest of every amount we need:

First to place the value of I in the 43000$ interest equation:

I₁ = 43000 x 6.078% = 2613,56

Second to place the value of I in the 37000$ interest equation:

I₂ = 37000 x (0.95x6.078%) = 37000 x 5.774% = 2136,42

To make sure that the % rate obtained was the correct answer:

I₁ + I₂ = 2613,56 + 2136,42 = 4749,98 approximately 4750$

As a result: the rate for 43000 $ is 6.078% and the rate of 37000 $ is 5.774%