5 years ago, the age of a father was 14 years more than twice his son's age. After how many years from now will he be twice his son's age?
Solution:
Let present ages be Father F and Son S.
5 years ago: F - 5 = 14 + 2(S - 5).
F-5 = 14 + 2(S-5)
F - 5 = 14 + 2S -10
F = 2S + 9.
Let after t years father is twice the son:
F + t = 2(S + t)
F - 2S = t.
Using F = 2S + 9:
(2S+9) - 2S = t
t = 9.
After 9 years.
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