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The first half of the question involves Daniel (D) and Alan (A).
Daniel is currently one fifth of Alan's age, so:
A = D x 5 (1)
In 21 years time, Alan will be twice his age, so:
A + 21 = (D + 21) x 2 (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 Daniel is 7 (and Alan is 35).
The second half of the question involves Jessica (J) and Betty (B).
Betty's is exactly seven times the age of Jessica:
B = J x 7 (3)
In 8 years time, Betty will be three times the age of Jessica, so:
B + 8 = (J + 8) x 3 (4)
Using (3) in (4) gives:
B + 8 = (J + 8) x 3
7J + 8 = (J + 8) x 3
7J + 8 = 3J + 24
4J = 16
J = 4
So Jessica is 4 (and Betty is 28).
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