Alex's child, Drew, is exactly one fifth of Alex's age. In 21 years, Alex will be exactly twice Drew's age. How old is Drew now?
Billie is exactly seven times the age of his child, Glen. In 8 years, Billie will be three times the age of Glen. How old is Glen now?
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Answers
Drew is 7 years old.
Glen is 4 years old.
Answer #1
The first question involves Drew (D) and Alex (A).
Drew is currently one fifth of Alex's age, so:
(1) A = D x 5
In 21 years, Alex will be twice their age, so:
(2) A + 21 = (D + 21) x 2
Using (1) in (2) gives:
A + 21 = (D + 21) x 2
5D + 21 = (D + 21) x 2
5D + 21 = 2D + 42
3D = 21
D = 7
So Drew is 7 (and Alex is 35).
Answer #2
The second question involves Glen (G) and Billie (B).
Billie is exactly seven times the age of Glen:
(3) B = G x 7
In 8 years, Billie will be three times the age of Glen, so:
(4) B + 8 = (G + 8) x 3
Using (3) in (4) gives:
B + 8 = (G + 8) x 3
7G + 8 = (G + 8) x 3
7G + 8 = 3G + 24
4G = 16
G = 4
So Glen is 4 (and Billie is 28).
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