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Let A = Alice's present age and J = John's present age.
1) A = J+8 "Alice is 8 years older than...John."
2) A+5 = 2(J+5) "In 5 years,she will be twice as old as John."
Substitute A = J+8 from equation 1) into equation 2) and solve for J.
2a) (J+8)+5 = 2(J+5) Simplify and solve for J
2b) J+13 = 2J+10 Subtract J from both sides.
2c) 13 = J+10 Subtract 10 from both sides.
2d) J = 3 and A = J+8 = 11
Alice is 11 years old and John is 3 years old.