# How old are Daniel and Jessica now?

Alan’s son Daniel, is exactly one fifth of Alan’s age.

In 21 years time, Alan will be exactly twice Daniel’s age.

Betty’s is exactly seven times the age of her daughter, Jessica.

In 8 years time, Betty will be three times the age of Jessica.

How old are Daniel and Jessica now?

Daniel is 7 years old and Jessica is 4 years old.

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). QED.

### Your Answer

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