Lilian has part of $9000 invested at 4% and the remainder at 6%. his annual return on each investment is the same. at what rate would she have to invest all her money to get the same interest?

Given:
Total amount invested = $9,000
interest rates = 4% and 6%

Let x be the part of 9,000.
Note that annual return on each investment is the same.

0.04x = 0.06(9,000 - x)
0.04x = 540 - 0.06x
0.04x + 0.06x = 540
0.10x = 540 
x = 540/0.10
x = 5,400

0.04x = 0.06(9,000 - x)
0.04(5,400) = 0.06(9,000 - 5,400)
216 = 0.06(3,600)
216 = 216

total interest for the year : 216 + 216 = 432

Interest = pricipal * interest rate * term
432 = 9,000 * interest rate * 1 yr
432/9,000 = interest rate
0.048 = interest rate

Interest rate would be 4.8% to get the same interest from the whole 9,000.