# Ladies' Diary/Ratios of Ages of Groom to Bride

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## Puzzle

*A person remarked that upon his wedding day the proportion of his own age to that of his bride was $3$ to $1$,**but $15$ years afterwards the proportion of their ages was $2$ to $1$.*

*What were their ages upon the day of their marriage?*

## Solution

The bride was $15$ and the groom was $45$ when they married.

Outrageous.

## Proof

Let $x$ and $y$ be the ages of the bride and groom at their marriage respectively.

We have:

\(\ds 3 x\) | \(=\) | \(\ds y\) | ||||||||||||

\(\ds 2 \paren {x + 15}\) | \(=\) | \(\ds y + 15\) | ||||||||||||

\(\ds \leadsto \ \ \) | \(\ds 2 x + 30\) | \(=\) | \(\ds 3 x + 15\) | |||||||||||

\(\ds \leadsto \ \ \) | \(\ds x\) | \(=\) | \(\ds 15\) | |||||||||||

\(\ds \leadsto \ \ \) | \(\ds y\) | \(=\) | \(\ds 45\) |

$\blacksquare$

## Sources

- 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): The Ladies' Diary or Woman's Almanac, $\text {1704}$ – $\text {1841}$: $138$