A woman went shopping. First she spent 4/5 of all money she had in her purse, and then she lost 2/3 of what was remaining. Now she has $10 left.

How much money did she lose

She lost $20

Step-by-step explanation:

This is a 2 step problem

Let's call x the total amount of money in her purse.

First, the woman spent 4/5 of her money - -> 4/5x

Then, she spent 2/3 of the remainder - -> (2/3) (4/5x)

Let's take the difference of her total and what she spent.

10 = x - ((4/5x) + ((2/3) (1/5x))) - -> combine like terms

10 = x - ((12/15x) + (2/15x))

10 = x - (14/15x)

10 = 1/15x

x = 10*15

x = 150

If she lost 2/15x

(2/15) (150) = 20