1510.21 – Pamela Gore

Pamela Gore, a well-traveled woman, lived $\dfrac{1}{2}$ of her life in Oklahoma, $\dfrac{1}{5}$ in Alaska, and $\dfrac{2}{9}$ in Idaho. She then moved to Miami and died 7 years later under unclear circumstances. How long did Pamela live?

Solution

Let $x$ represent the length of Pamela's life.

$\dfrac{x}{2} + \dfrac{x}{5} + \dfrac{2x}{9} + 7 = x$

$\dfrac{(45 + 18 + 20)x}{90} + 7 = x$

$\dfrac{83x}{90} + 7 = \dfrac{90x}{90}$

So $7 = \dfrac{7x}{90}$ and $x = 90$ , a wonderful old age.