## 1540.33 – Hattie's Age in 1900

Hattie's age at her death was exactly $1/29$ of the year of her birth. How old was she in 1900?

## Solution

We need to look at the exact multiples of 29 in the 1800's. One of them is the year of Hattie's birth. There are three possibilities:

$29 \times 63 = 1827;\hspace{.1in} 29 \times 64 = 1856; \hspace{.1in} 29 \times 65 = 1885$. That's all there are.

If she was born in 1827, then she died in 1827 + 63 = 1890. That is too soon. If she was born in 1856, then she died in 1856 + 64 = 1920. That works. If she was born in 1885, then she died in 1885 + 65 = 1950. That also works.

So Hattie was either 44 or 15 in 1900.