Alex deposited x dollars into a new account…
We start by determining the new value of the x dollars Alex deposited into his account that earned 8 percent annual interest. At the end of the first year the amount of money in the account was 1.08x and then he added another x dollars to the account, so the account now had a total value of 1.08x + x dollars. The 1.08x + x dollars earned another 8 percent interest for the year. Thus, the total value of his account at the end of the second year is:
1.08(1.08x + x) = (1.08^2)x + 1.08x
Since the new total value is equal to w, we can set up the following equation:
w = (1.08^2)x + 1.08x
Now we must get x in terms of w.
w = x(1.08^2 + 1.08)
w/(1.08^2 + 1.08) = x