# A man is 4 times as old as his son. In 3 years, the father will be 3 times as old as his son. How old is each of them now?

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Right now, the man is 24 and his son is 6. Here is how you figure this out:

Let the man's age by M and the son's age be S.

Right now M = 4S

In three years

M + 3 = 3(S + 3)

So you put the 4S in to substitute for the M.

4S + 3 = 3(S + 3)

4S + 3 = 3S + 9

**S = 6**

If the son is 6, the father must be 24.

We can check this by adding three to both ages. Then, the son will be 9 and the father will be 27, which is three times 9.

Assume that the son's age = x

then the man age = 4 times as old ad his son = 4x

after 3 years:

the son age = x+3

the man age = 3 times as old as his son = 3(X+3)

but 3 years later, the man age was 4x so now his age is 4x+3

then 3(x+3) = 4x +3

==> 3x+9 = 4x +3

==> 6 = x

then the son age now = 6

and the man age = 4(6) = 24

after 3 years, the son will be 9

and the father will be 24+3 = 27 or 3(9)= 27

Let's establish the followings:

a = the age of the son, now

b = the age of the father, now.

a+3 = the age of the son, after 3 years.

b+3 = the age of the father, after 3 years.

Now, the father's age is 4 times the son's age.

b = 4a (1)

After 3 years, the father's age will be:

b+3 = 3(a+3) (2)

We'll substitute the equation (1) into the equation (2).

4a+3 = 3a + 9

4a - 3a = 9-3

a = 6

b = 4*6

b = 24

The son is 6 years old and his father is 27 years old, now.

Let he sun's age now be x years

Then the father's age is by data = 4 times sun's age = 4x years.

After 3 years the ages of sun and father are: x+3 y and 4x+3y respectively.

By by data the father will be 3 times as old as son after 3 years. So : 4x+3 = 3 (x+3). Solving for x gives the age of the son. So

4x+3 = 3x+9 Or

4x-3x = 9-3 =6. Or

x =6. So the age of the sun now = x = 6 years. And the age of the father now = 4x = 4*6 = 24.

Tally after 3 years Son and father attain 9 years and 27 years . So the father' age will be 3 times sons age ,i.e 27 =3*9