Fatuma invests a total of $11,000 in two accounts paying 9% and 6% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $780.00. How much money was in each account at 9% and 6%?

If she invested x in the first account, then she invested 11000 - x in the second account.

The first accound earned 9% of x = 0.09x in a year and the second account earned 6% of (11000-x), that is, 0.06(11000 - x). Given the total interest, we can write the equation:

0.09x + 0.06(11000 - x) = 780;

0.09x + 660 - 0.06x = 780;

0.03x = 780 - 660 = 120, and x = 120 / 0.03 = 4000.

Answer $4000 in the first account and $7000 in the second account.