Question

The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary. What is the present age of each?

Answer 1

John is `20`
Mary `12`

Explanation:

let John's age be `x` and Mary's age be `y`
so `x+y=32`

now `4` years ago John was `x-4` and Mary was `y-4`

so according to the problem

`x-4=2(y-4)`

solving the two equations we get John's age as `20` years and Mary's age as `12` years

Answer 2

Mary's age is `12` and John's age is `20`

Explanation:

We can use one variable to define their ages because we know the relationship between their ages.

Mary is younger, let Mary's present age be `x` years,

Then John's present age is `32-x` years (Sum of their ages is `32` )

`4` years ago, they were both `4` years younger than now.

Mary was `(x-4)` and John was `(32-x-4) = (28-x)` years old.
John was twice as old as Mary:

`2(x-4) = 28-x`

`2x -8 = 28-x`

`3x = 28+8`

`3x = 36`

`x=12`

Mary's age is `12` and John's age is `20`