Awoman 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

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