Respuesta :
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
[tex]Money\ spent = \frac{2x}{3}[/tex]
Money she had after spent two thirds of her money = Total money - money spent
[tex]= x - \frac{2x}{3}[/tex]
[tex]= \frac{1x}{3}[/tex]
As given she lost two thirds the remainder
[tex]=\frac{2}{3}\times ( money\ she\ had\ after\ spending\ two\ thirds\ of\ her\ money)[/tex]
[tex]= \frac{2}{3} \times\frac{1x}{3}[/tex]
we get
[tex]=\frac{2x}{9}[/tex]
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
[tex]= \frac{1x}{3} - \frac{2x}{9}[/tex]
[tex]= \frac{1x}{9}[/tex]
As given
she had $4 left
thus
[tex]\frac{1x}{9} = 4[/tex]
x = $36
she start with $36.
Hence proved
Let the woman started with = x
She spent money = [tex]\frac{2}{3}[/tex] of x
She lost money = [tex]\frac{2}{3}[/tex] of [tex]x-\frac{2}{3}[/tex]
Equation becomes =
[tex]x-\frac{2x}{3}-\frac{2}{3}(x-\frac{2x}{3})=4[/tex]
[tex]x-\frac{2x}{3}-\frac{2x}{9}=4[/tex]
[tex]\frac{9x-6x-2x}{9}=4[/tex]
[tex]\frac{x}{9}=4[/tex]
[tex]x=36[/tex]
Hence she started with $36.
