Ladies' Diary/Age Problem

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Puzzle

If to my age there added be,
One half, one third, and three times three,
Six score and ten the sum you'll see,
Pray find out what my age will be.


Solution

Let $x$ be the age to be found.

Translating from flowery language into an algebraic expression, we get:

\(\ds x + \dfrac x 2 + \dfrac x 3 + 3 \times 3\) \(=\) \(\ds 6 \times 20 + 10\)
\(\ds \leadsto \ \ \) \(\ds \dfrac {11 x} 6\) \(=\) \(\ds 130 - 9\)
\(\ds \leadsto \ \ \) \(\ds x\) \(=\) \(\ds \dfrac {6 \times 121} {11}\)
\(\ds \) \(=\) \(\ds 66\)

$\blacksquare$


Sources