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
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Ladies' Diary or Woman's Almanac, $\text {1704}$ – $\text {1841}$: $137$