Step 1 :Let's denote the amount of money invested at 1.7% as x, and the amount of money invested at 2.3% and 2.4% as y each.
Step 2 :We know that the total amount invested is $25,000, so we have the equation \(x + 2y = 25000\).
Step 3 :We also know that the total annual interest earned was $555, so we have the equation \(0.017x + 0.047y = 555\).
Step 4 :We can solve these two equations to find the values of x and y.
Step 5 :The solution to the system of equations is \(x = 5000\) and \(y = 10000\).
Step 6 :Final Answer: At the rate $1.7 \%$, \(\boxed{\$ 5000}\) was invested. At the rates $2.3 \%$ and $2.4 \%$, \(\boxed{\$ 10000}\) was invested each.