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

Answer:

$140

Step-by-step explanation:

10 is 1/3 of x.

10=1/3x

x=30

x is 1/5 of y

30=1/5y

150=y

y-10=z

150-10=z

z=140

Answer 2

Answer:

$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