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#. 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(r + 6)#

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

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

#r + 18 + 6 = 2r + 12#

#r + 24 = 2r + 12#

#r - r + 24 - 12 = 2r +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#