Question

A man is four times as older as his son. In four years time he will be three times as old. What are their ages now?

Answer 1

Present age of son: 8 years.

Present age of father: 32 years.

Explanation:

Let x represent present age of the son and y represent present age of father.

We have been given that a man is four times as older as his son. 4 times of age of son would be
`4x`.

We can represent this information in an equation as:

`y=4x`

We are also told that in four years time he will be three times as old.

Age of father in 4 years would be
`y+4`.

We can represent this information in an equation as:

`y+4=3(x+4)`

Upon substituting
`y=4x` in 2nd equation, we will get:

`4x+4=3(x+4)`

`4x+4=3x+12`

`4x+4-4=3x+12-4`

`4x=3x+8`

`4x-3x=3x-3x+8`

`x=8`

Therefore, the present age of son is 8 years.

Upon substituting
`x=8` in equation
`y=4x`, we will get:

`y=4x\Rightarrow 4(8)=32`

Therefore, the present age of father is 32 years.

Answer 2

The son is 8 years old

The father is 32 years old

Explanation:

Let the man age be x

Let the son age = y

Right now the man is four times as older as his son = x=4y

In four years time he will be three times as old. ⇒x+4 =3(y+4)

Now substitute the value x=4y in x+4=3(y+4)

x+4=3(y+4)

4y+4=3(y+4)

4y+4=3y+12

Combine the like terms:

4y-3y =12-4

y=8

If the son is 8 years old than;

x=4y

x=4(8)

x=32

Father will be 32 years old....