With how much money did she start?

A woman spent two-thirds of her money. She lost two-thirds of the remainder and then had $4 left. With how much money did she start?

Let M be the money the woman had with her initially.

The money she spent = \(\dfrac{2}{3}\) * M
Remaining = M -  \(\dfrac{2}{3}\) * M =  \(\dfrac{1}{3}\) * M
The money she lost =  \(\dfrac{2}{3}\) * ( \(\dfrac{1}{3}\) * M ) = \(\dfrac{2}{9}\) * M
Remaining = \(\dfrac{1}{3}\) * M - \(\dfrac{2}{9}\) * M= \(\dfrac{1}{9}\) * M

=> \(\dfrac{1}{9}\) * M = 4
=> M = 9 * 4 = 36

She had $36 at the start.