An investor deposited some money at $1.7 \%$ annual interest, and two equal but larger amounts at $2.3 \%$ and $2.4 \%$. The total amount invested was $\$ 25,000$, and the total annual interest earned was $\$ 555$. How much was invested at each rate?
At the rate $1.7 \%, \$ \square$ was invested.
Answer
Final Answer: At the rate $1.7 \%$, \(\boxed{\$ 5000}\) was invested. At the rates $2.3 \%$ and $2.4 \%$, \(\boxed{\$ 10000}\) was invested each.
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.
