Question

3. Your father gives one-half of the money in his pocket to your mother, one-fourth of what is left to your brother, and one-third of what then remains to your sister. He then splits the rest with you. If you get $4.00, how much did your father start with?​

Answer 1

The father start with $16

Explanation:

Let

x -----> the original amount of money

step 1

Your father gives one-half of the money in his pocket to your mother

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

The remaining is

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

step 2

Your father gives, one-fourth of what is left to your brother

`((1)/(4))(1)/(2)x=(1)/(8)x`

The remaining is

`(1)/(2)x-(1)/(8)x=(3)/(8)x`

step 3

Your father gives one-third of what then remains to your sister

`((1)/(3))(3)/(8)x=(3)/(24)x`

The remaining is

`(3)/(8)x-(3)/(24)x=(6)/(24)x=(1)/(4)x`

step 4

Your father gives the rest with you

`(1)/(4)x=\$4`

`x=\$16`

therefore

The father start with $16