Question 1199026
x = the mother's age today.
y = the son's age today.


4 years ago, the mother was 4 times as old as her son.
the equation for that is:
(x - 4) = 4 * (y -4)
simplify to get:
x - 4 = 4 * y - 16
solve for x to get:
x = 4 * y - 12


in 4 years time, the sum of their ages will be 56.
the equation for that is:
x + 4 + y + 4 = 56
combine like terms to get:
x + y + 8 = 56
solve for x + y to get:
x + y = 48


replace x in the second equation with 4 * y - 12 from the first equation to get:
4 * y - 12 + y = 48
combine like terms and add 12 to both sides of the equation to get:
5 * y = 60
solve for y to get:
y = 12


since x + y = 48, then x = 36.
the mother's age is currently 36
the son's age is currently 12


4 years ago, the mother was 32 and the son was 8.
32 is 4 * 8.
in 4 years time, the mother will be 40 and the son will be 16.
40 + 16 = 56.
the requirements of the problem are satisfied when the mother's current age is 36 and the son's current age is 12.


the son was born 12 years ago.
12 years ago, the mother was 24.
the mother was 24 years old when the son was born.
that's your solution.