Question

A is elder to B by two years. A's father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and the sister differs by 40 years, find the age of A?

Answer 1

`A` is 26 years old.

Explanation:

The idea here is that you can use the information given to you to write four equations with four unknows, `A`, `B`, `C`, and `D`.

So, you know that `A` is two years older than `B`, which means that you can write

`A = B + 2 " "color(blue)((1))`

You also know that `A`'s father, `F`, is twice as old as `A`

`F = 2 * A" "color(blue)((2))`

The same can be said for `B` and his sister `S`

`B = 2 * S" "color(blue)((3))`

FInally, you know that the difference between the ge of the father nad the age of the sister is 40 years old, so you can write

`F - S = 40" "color(blue)((4))`

Now you can replace `F` from equation `color(blue)((2))` into equation `color(blue)((4))` and `B` from equation `color(blue)((3))` into equation `color(blue)((1))` to write

`{(A = 2S + 2), (2A - S = 40) :}`

Replace the value of `A` from the first equation into the second one to get

`2 * (2S + 2) - S = 40`

`4S - S + 4 = 40`

`3S = 36 implies S = 36/3 = 12`

This means that the age of `A` is

`A = 2 * S + 2`

`A = 2 * 12 + 2 = color(green)(26)`