Question

Question #b9e5a

Answer 1

The Father is now `40` and Mary is `10`.

Explanation:

Let us say the current Mary is `M` and her current father is `F`.

1) In the present:

`F = 4M`

Mary’s father is four times as old as Mary.

2) Using the terms above, the equation of their age `5` years ago is this:

`F - 5 = 7(M-5)`

The father is `5` years younger and is `7` times older than Mary was `5` years ago.

3) Remove the brackets from the previous equation, simplify it and bring it into the terms of `F`.

`i) " "F - 5 = 7M - 35`

`ii) " "F = 7M - 30`

4) Piece it all together.

`7M - 30 = 4M`

`3M - 30 = 0`

`3M = 30`

`M = 10`

We already know that `F = 4M`, and we just worked out that F also `= 7M - 30`. This means `4M` and `7M - 30` is the same. After working it all out, we see `M = 10`.

5) Double check by substituting.

`M = 10`

`F = 4M = 40`

`F - 5 = 35`

`M - 5 = 5`

`5 xx 7 = 35`

It all works out...

6) All Done! I hope I helped.

Answer 2

She is `10` now and he is `40`

Explanation:

There are two people: Mary and her Father

and two periods of time: present and `5` years ago.

Write an expression for each person for each period of time:

Mary is younger, so let her present age be `x`
Her father is `4` times older, so his present age is `4x`

Five years ago, they were both younger by `5` years

Mary's age was `x-5`
Her father was `4x -5`

However, `5` years ago, he was `7` times as old as she was.

Write this as an equation.

`7(x-5) = 4x-5`

`7x -35 = 4x-5`

`7x-4x = 35-5`

`3x = 10`

`x =10`

She is `10` now and he is `40`

`5` years ago .... She was `5` and he was `35`

`7 xx 5 = 35`