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This problem trains for: SAT-I, GMAT, AMC-8, Math Kangaroo 3-4, Math Kangaroo 5-6.

Joe Gargery was 22 years older than Pip. At some point in the story, Pip left Joe. Ten years later, Joe would be twice as old as Pip. How old was Pip when he left Joe?

(characters from Charles Dickens' "Great Expectations")

The difference in ages remains the same throughout their lives.

Denote Pip's age before leaving by x.

After 10 years, Pip would be:

equation

and Joe's age would be:

equation

Additionally, Joe's age would be twice Pip's:

equation

Solve for x.

equation

equation

Pip was 12 years old when he left Joe's home.