Question

A woman went shopping. First she spent 4/5 of all the 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 spend?

Answer 1

To find out how much money the woman spent, we need to determine the amount she had in her purse and then calculate the difference after spending and losing some. We can solve this using a step-by-step approach.

Step-by-step explanation:

To calculate how much money the woman spent, we need to follow these steps:

1. First, she spent 4/5 of all the money she had in her purse. Let's call this amount X.
2. After spending 4/5 of X, she lost 2/3 of what was remaining. This means she has 1/3 of what was remaining left. Let's call this amount Y.
3. We know that Y is equal to $10. So, we can set up the equation Y = $10 and solve for X.
4. Once we find X, we can calculate how much money the woman spent by subtracting X from the original amount she had in her purse.

Let's solve this step-by-step:

Step 1: X = Amount she had in her purse

Step 2: Y = (4/5) * X * (1/3)

Step 3: Y = $10

Step 4: Calculate X - Y to find how much money she spent.

Answer 2

$120

Step-by-step explanation:

Suppose the woman had x dollars in her purse at the beginning of the shopping.

First, she spent 4/5 of all the money she had, therefore she had 1-4/5=1/5 left

1/5 of x = (1/5)x or 0.2x

Then she lost 2/3 of what was remaining, which is 2/3 * (1/5)x= (2/15)x

What will be left will be (1-2/3) or 1/3 of that 1/5x left after shopping.

This will be 1/3*(1/5)x=(1/15)x

It is given from the problem statement that this is $10 left.

Therefore, (1/15)x= 10

Multiplying through by 15 and simplifying,

x= $150.

Now she spent 4/5 of this $150, which is

(4/5)*150=$120