Question 585418
Let the ages of Mary and John be x and y years respectively today.

3 years ago, age of John was (y-3) years

Since Mary is twice as old as john was 3 years ago.
So,  x = 2(y-3)
 or  x = 2y - 6   -------- (1)

In 5 years, age of John will be = (y + 5) years

"John will be 1 year older than Mary is now"

So,    (y+5) = x + 1
or   x = y + 5 -1
or  x = y + 4     --------(2)

Using equation (1) and (2),  we get:

2y - 6 = y + 4
2y = y + 4 + 6
2y = y + 10
y = 10


Plugging back the value of y in equation (2)

x = 10 + 4
x = 14


Hence, Age of Mary today is x= 14 years and age of John today is y=10 years.

Hope this helps~!