Explanation:
Let's assume the amount invested at 3% per year is x dollars.
According to the given information, the amount invested at 10% per year would then be (38500 - x) dollars.
The annual income from the 3% investment would be 0.03x dollars, and the annual income from the 10% investment would be 0.10(38500 - x) dollars.
Given that the total annual income is 2590 dollars, we can set up the equation:
0.03x + 0.10(38500 - x) = 2590
Simplifying the equation, we get:
0.03x + 3850 - 0.10x = 2590
Combining like terms, we have:
-0.07x + 3850 = 2590
Subtracting 3850 from both sides, we get:
-0.07x = -1260
Dividing both sides by -0.07, we get:
x = -1260 / -0.07
x = 18000
Therefore, $18,000 is invested at a 3% rate, and $20,500 (38500 - 18000) is invested at a 10% rate.