Smith sold 4/5 of his dvds and purchased 10 more. if smith has 15 dvds now, how many dvds did he have to begin with?

To do this, we must work through the problem backwards.
Smith has 15 now, however the last thing he did was buy 10 (+10)
To go back a step we must do the opposite of add 10, subtract 10
15 - 10 = 5
Smith sold 4/5 of his DVDs to leave him with 5
This means that 1/5 = 5
1/5 of the original amount was equal to 5
To make 5/5 (or a whole) we multiply by 5
5 x 5 = 25
Smith has 25 DVDs to begin with