What are their ages now?

Gina is 3 years older than Ana.  Six years ago she was twice as old.  What are their ages now?

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x = Ana’s age right now
x + 3 = Gina’s age right now   {Gina is 3 years older than Ana (right now)}

x - 6 = Ana’s age 6 years ago   {subtracted 6 from Ana’s current age, above}
x - 3 = Gina’s age 6 years ago   {subtracted 6 from Gina’s current age, above}

x - 3 = 2(x - 6)   {six years ago, Gina (x - 3) was twice as old as Ana (x - 6)}
x - 3 = 2x - 12   {used distributive property}
x = 9   {subtracted x from and added 12 to each side}
x + 3 = 12   {substituted 9, in for x, into x + 3}

Ana is 9 now
Gina is 12 now

Ana was 3 six years ago
Gina was 6 six years ago  {twice as old as Ana}

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