Question

A woman spent two thirds of her money she lost two thirds the remainder and then had $4 left how much money did she start with

Answer 1

Let the woman started with = x

She spent money =
`(2)/(3)` of x

She lost money =
`(2)/(3)` of
`x-(2)/(3)`

Equation becomes =

`x-(2x)/(3)-(2)/(3)(x-(2x)/(3))=4`

`x-(2x)/(3)-(2x)/(9)=4`

`(9x-6x-2x)/(9)=4`

`(x)/(9)=4`

`x=36`

Hence she started with $36.

Answer 2

Find out how much money did she start with.

To proof

let us assume that the money she had be x.

As given

woman spent two thirds of her money

`Money\ spent = (2x)/(3)`

Money she had after spent two thirds of her money = Total money - money spent

`= x - (2x)/(3)`

`= (1x)/(3)`

As given she lost two thirds the remainder

`=(2)/(3)* ( money\ she\ had\ after\ spending\ two\ thirds\ of\ her\ money)`

`= (2)/(3) *(1x)/(3)`

we get

`=(2x)/(9)`

Money she had after lost two thirds the remainder = Money she had after spent two thirds of her money - she lost two thirds the remainder

`= (1x)/(3) - (2x)/(9)`

`= (1x)/(9)`

As given

she had $4 left

thus

`(1x)/(9) = 4`

x = $36

she start with $36.

Hence proved