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 = $\frac{2}{3}$ of x

She lost money = $\frac{2}{3}$ of $x-\frac{2}{3}$

Equation becomes =

$x-\frac{2x}{3}-\frac{2}{3}(x-\frac{2x}{3})=4$

$x-\frac{2x}{3}-\frac{2x}{9}=4$

$\frac{9x-6x-2x}{9}=4$

$\frac{x}{9}=4$

$x=36$

Hence she started with $36.

Answer 2

Answer

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

$Money\ spent = \frac{2x}{3}$

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

$= x - \frac{2x}{3}$

$= \frac{1x}{3}$

As given she lost two thirds the remainder

$=\frac{2}{3}\times ( money\ she\ had\ after\ spending\ two\ thirds\ of\ her\ money)$

$= \frac{2}{3} \times\frac{1x}{3}$

we get

$=\frac{2x}{9}$

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

$= \frac{1x}{3} - \frac{2x}{9}$

$= \frac{1x}{9}$

As given

she had $4 left

thus

$\frac{1x}{9} = 4$

x = $36

she start with $36.

Hence proved