# My father is four times as old as me. In 20 years, he will be only twice as old as me How is my father and how old am l?

Nov 16, 2016

I got that you are $10$ years old while your father is $40$ years old.

#### Explanation:

Let us call the age of your father $x$ and your's $y$; we can write:
$x = 4 y$
$x + 20 = 2 \left(y + 20\right)$

we have, substituting the first into the second:
$4 y + 20 = 2 y + 40$
$2 y = 20$
$y = \frac{20}{2} = 10$
so that:
$x = 4 \cdot 10 = 40$

Nov 16, 2016

I am currently 10 years old and my father is currently 40 years old.

#### Explanation:

Let's let my age be $m$.

So right now my father's age, Let's call it $n$ is $4 m$ or

$n = 4 m$.

So in 20 years I will be $m + 20$ years old and my father will be $n + 20$ years old. But at this time he will be only twice as old as me. So we can right an equation for our age in 20 years as:

$n + 20 = 2 \left(m + 20\right)$

Substituting $4 m$ from the first equation for $n$ in the second equation and solving for $m$ while keeping the equation balanced gives:

4m + 20 = 2(m + 20

$4 m + 20 = 2 m + 40$

$4 m + 20 - 2 m - 20 = 2 m + 40 - 2 m - 20$

$2 m = 20$

$\frac{2 m}{2} = \frac{20}{2}$

$m = 10$

So my age is currently 10 years old.

Substituting 10 for $m$ is the first equation gives:

$n = 4 \cdot 10$

$n = 40$

Nov 16, 2016

I am 10 years old now and and my father is 40.

#### Explanation:

Although we are dealing with the ages of two people, we only need to use one variable, because we know how their ages are connected.

Let my present age be $x , \text{ }$ then my father's age is $4 x$

In 20 years time
My age will be $x + 20$ and my father's age will be $4 x + 20$

Then, twice my age will be the same as my father's age.

"2 x younger age = older age"
Do not make the mistake of doubling the father's age!

$2 \times \left(x + 20\right) = 4 x + 20$

$2 x + 40 = 4 x + 20$

$40 - 20 = 4 x - 2 x \text{ } \leftarrow$ keeping x positive

$20 = 2 x$

$10 = x$