# Greg is 18 years older than his sister Gloria. In 6 years, he will be twice as old as Gloria. How old is each of them now?

Nov 30, 2016

Greg is 30 and Gloria is 12

#### Explanation:

Let's call Greg's age now $g$. And, Let's call Gloria's age now $r$.

We are told Greg is now 18 years older than Gloria. So, we can write:

$g = r + 18$

We also know in 6 years (g + 6) he will be twice as old as Gloria. So we can write:

$g + 6 = 2 \left(r + 6\right)$

From the first equation we can substitute $r + 18$ for $g$ in the second equation and solve for $r$:

$\left(r + 18\right) + 6 = 2 \left(r + 6\right)$

$r + 18 + 6 = 2 r + 12$

$r + 24 = 2 r + 12$

$r - r + 24 - 12 = 2 r + 12 - r - 12$

$24 - 12 = r$

$r = 12$

Now that we know Gloria is 12 we can calculate Greg's age by substituting $12$ for $r$ in the first equation and calculating $g$:

$g = 12 + 18$

$g = 30$