Nicholas and Nicole saved the same amount of money. After Nicholas lent $82 to Nicole, Nicole had 5 times as much money as Nicholas. How much did Nicole have in the end?

Let d = initial amount that both have. We are told that:

d + 82 = 5*(d - 82)

d + 82 = 5d -5*82

Subtract d from both sides and add 5*82 to both sides to get

6*82 = 4*d

so d = 6*82/4 = $123

Hence final amount Nicole had = $123 + $82 = $205