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?

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Answer 1 · 2018-06-03T19:14:49

John is $20$
Mary $12$

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 · 2018-06-03T20:26:48

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

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 $20$