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?

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Answer 1 · 2016-11-30T03:00:14

Greg is 30 and Gloria is 12

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

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

$g = r + 18$ $g = r + 18$

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

$g + 6 = 2 (r + 6)$ $g + 6 = 2(r + 6)$

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

$(r + 18) + 6 = 2 (r + 6)$ $(r + 18) + 6 = 2(r + 6)$

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

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

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

$24 - 12 = r$ $24 - 12 = r$

$r = 12$ $r = 12$

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

$g = 12 + 18$ $g = 12 + 18$

$g = 30$ $g = 30$