Lesson A fresh formulation of a traditional age problem

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A fresh formulation of a traditional age problem

This problem is intended and designed to make you smile =:)
It also proves that even very traditional age problem can go in a very attractive fresh formulation.

Problem

In a film an actor plays an "uncle", he was being criticized for marrying a woman when he is three times her age.
He then replied: "Oh, but in 20 years time I will only be twice her age." How old are the "uncle" and the woman?

Solution

Let w be the woman's present age, and m be the actor's present age.

Then according to the condition, you have these two equations:

m = 3w                     (man's age is three times that of the woman).
m + 20 = 2(w+20).     (20 years later)

So you have the system of two equations in two unknowns:

m = 3w,                       (1)
m + 20 = 2(w+20).       (2)

Substitute m = 3w from (1) into (2). You will get

3w + 20 = 2(w+20),     or   3w + 20 = 2w + 40,     or   w = 40-20 = 20.

Answer. The woman is 20 years now. The actor is 60 years now.

My other lessons on age word problems in this site are
    - Age problems and their solutions
    - HOW TO algebraize and to solve age problems?
    - Intricate age word problems
    - Challenging age word problems
    - Age problems for mental solution
    - Age problem for three participants
    - Some unusual age word problems
    - Age problems with a defective sum of ages
    - Miscellaneous age problems
    - Entertainment age problems
    - Age problem for the day of April, 1
    - OVERVIEW of lessons on age problems

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

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