Past Political Life

In 1999, while collecting information on an important politician figure, I found that his age at death was one thirty-ninth of the year of his birth. How old was the politician in 1921?
Source: mathcontest.olemiss.edu 2/11/2008

SOLUTION
Let x be the year of birth. Let y be the year of death. Then, age at death equals y-x and we have the following equation:
y-x=x\div 39        (1)

We have the following facts:
1. x is a multiple of 39 because y-x is a whole number
2. x<1921
3. y>1921

Rewrite Eq. (1) and apply a few numbers for age at death y-x:
39\times \left (y-x\right )=x
39\times 47=1833
39\times 48=1872
39\times 49=1911
39\times 50=1950

We eliminate x=1833 because y=1833+47=1880\ngtr 1921. Likewise, we eliminate x=1872 because y=1872+48=1920\ngtr 1921.

We also eliminate x=1950 because 1950\nless 1921.

The process of elimination leaves us with the solution:
Year of birth x=1911<1921
Year of death y=1911+49=1960>1921
Thus, the politician’s age in 1921 is 1921-1911=10.

Answer: 10.

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About mvtrinh

Retired high school math teacher.
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