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In a​ film, a character is criticized for marrying a woman when he is three times her age. He wittily​ replies, "Ah, but in 25 years time I shall only be twice her​ age." How old are the man and the​ woman?

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marcthemathtutor

Answer:

man = 75 years

woman = 25 years

Step-by-step explanation:

let the Man's age be M and Woman's age be W

Today: man is three times woman's age

i.e  M = 3W -----------(eq 1)

in 25 years,

man's age = M + 25

woman's age = W + 25

given: Man's age in 25 years will be twice woman's age

M+ 25 = 2 (W + 25)

M + 25 = 2W + 50   (subtract 25 from both sides)

M = 2W + 50 - 25

M = 2W + 25 -------------(eq 2)

substituting (eq 1) into (eq 2)

3W = 2W +25  (subtract 2W from both sides)

3W - 2W = 25  

W = 25  (substitute into eq 1 to get man's age)

M = 3(25) = 75

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