# Mark is 11 years older than his sister. In 8 years he he will be twice as old as she will be then. How old are they now?

Dec 13, 2016

Mark is 14 years old and his sister is 3 years old.

#### Explanation:

Let's call Mark's age now $m$

Let's call his sister's age now $s$

We know now Mark is 11 years older than his sister or:

$m = s + 11$

In 8 years, so $m + 8$ and $s + 8$ years. So we can write:

#m + 8 = 2(s + 8)

We already have the first equation in terms of $m$. So, we can substitute $s + 11$ for $m$ in the second equation and solve for $s$:

$s + 11 + 8 = 2 \left(s + 8\right)$

$s + 19 = 2 s + 16$

$s - s + 19 - 16 = 2 s - s + 16 - 16$

$0 + 3 = s$

$s = 3$

We can now substitute $3$ for $s$ in the first equation and calculate $m$:

$m = 3 + 11$

$m = 14$