A woman spent 2/5 of her money. She lost 2/3 of the remaining and then she had $8 left. With how much money did she start?
To determine the amount of money she started with, we can work backward from the given information.
Let's assume her initial amount of money is "x" dollars.
According to the information provided, she spent 2/5 of her money, so the remaining amount is (1 - 2/5) * x:
Remaining amount = (3/5) * x
Next, she lost 2/3 of the remaining amount, so the final amount she has is (1 - 2/3) * (3/5) * x:
Final amount = (1/3) * (3/5) * x = (1/5) * x
Based on the given information, the final amount is $8, so we can set up the equation:
(1/5) * x = 8
To solve for x, we multiply both sides of the equation by 5:
x = 8 * 5
x = 40
Therefore, the woman started with $40.
3/5 * 1/3 * x = 8
x = 8 * 15 / 3
x = 40
================
check:
2/5 * 40 = 16 spent, 24 left
2/3 * 24 = 16 spent, 8 left --- sure enough