A person invested $10000. the grater part is invested at 6% and the remainder at 5%. The annual income for the graterpart is $160more thsn the annual income from the smaller part . $4000 is the smaller part of the investment.
Solution

The annual income from the greater part invested at 6% is (10,000 - x) * 0.06 = 600 - 0.06x dollars.

The annual income from the smaller part invested at 5% is x * 0.05 = 0.05x dollars.

According to the problem, the annual income from the greater part is $160 more than the annual income from the smaller part.

So, we can set up the equation:

600 - 0.06x = 0.05x + 160

Simplifying the equation:

600 - 160 = 0.05x + 0.06x

440 = 0.11x

Dividing both sides of the equation by 0.11:

x = 440 / 0.11

x 4000