One year, Lucia invested a total of $40,000, part at 4%, part at 5%, and the rest at 5.5%. The total amount of interest received on the investments was $1990. The interest received on the 5.5% investment was $590 more than the interest received on the 4% investment. How much was invested at each rate? Show and explain each step including how you came up with the equations. Show all the work to solve the application.