Two investments totaling $35,500 produce an annual income of $2740 . One investment yields 8% per year, while the other yields 3% per year. How much is invested at each rate?

Let's assume the amount invested at 8% per year is x dollars.
Then, the amount invested at 3% per year would be (35,500 - x) dollars.

The annual income from the investment at 8% would be x multiplied by 8% (or 0.08).
Similarly, the annual income from the investment at 3% would be (35,500 - x) multiplied by 3% (or 0.03).

Given that the total annual income is $2,740, we can set up the following equation:

0.08x + 0.03(35,500 - x) = 2,740

Let's solve this equation to find the value of x.

0.08x + 0.03(35,500 - x) = 2,740
0.08x + 1,065 - 0.03x = 2,740
0.05x + 1,065 = 2,740
0.05x = 2,740 - 1,065
0.05x = 1,675
x = 1,675 / 0.05
x = 33,500

Therefore, $33,500 is invested at 8% per year, and $35,500 - $33,500 = $2,000 is invested at 3% per year.

Answer: $33,500 is invested at 8% per year, and $2,000 is invested at 3% per year.