The sum of John's age and twice of his son's age is 56. In 8 years time, the son's age will be half of john's age. Find there present ages.

Right now I wrote down an equation x+2y=56 and not quite sure what to do next.

OK. That's the first sentence covered in x+2y=56 .

In 8 years time, the son's age will be half of john's age.

If x is John's age now, then his age in 8 years is (x+8), and his son's will be (y+8).

So the next thing is to make a second equation from that sentence, using (x+8) and (y+8) for the ages.

x=20 and y=18

To solve the problem, you need to set up a system of equations based on the given information.

Let's use x to represent John's age and y to represent his son's age.

From the given information, we can set up two equations:

1) "The sum of John's age and twice of his son's age is 56":
x + 2y = 56

2) "In 8 years time (in the future), the son's age will be half of John's age":
y + 8 = (1/2)(x + 8)

Now you have a system of two equations. To solve it, you can use substitution or elimination method.

Let's start with solving it using the substitution method.

From equation 1, we have x + 2y = 56. We can solve this equation for x and express it in terms of y:
x = 56 - 2y

Now, substitute this expression for x into equation 2:
y + 8 = (1/2)(x + 8)

Replace x with 56 - 2y:
y + 8 = (1/2)((56 - 2y) + 8)

Simplify and solve for y:
y + 8 = (1/2)(64 - 2y)
2(y + 8) = 64 - 2y
2y + 16 = 64 - 2y
4y = 48
y = 12

Now that we have the value of y, we can substitute it back into equation 1 to find x:
x + 2(12) = 56
x + 24 = 56
x = 32

Therefore, John's present age (x) is 32 and his son's present age (y) is 12.