## 1510.22 – Pebble's Long Life

Pebble lived one twelfth of his life as a small child and one sixth more as a young adult. He then married Bloomie and lived happily for one seventh of his life plus five years. They then had a son, Nelius, who, sadly, Pebble outlived by four years. Nelius lived to be half of Pebble’s final age. How old was Pebble when he died?

## Solution

Suppose Pebble lived $x$ years. Then Nelius lived $x/2$ years. To find Pebble’s final age, simply add the given bits together and perform some basic algebra.

$\begin{aligned}
\frac{x}{12} + \frac{x}{6} +\frac{x}{7} + 5 +\frac{x}{2} +4 &=& x, \\
\frac{7x}{84} + \frac{14x}{84} +\frac{12x}{84} + 5 +\frac{42x}{84} +4 &=& x, \\
\frac{75x}{84} + 9 &=& x, \\
\frac{75x}{84} &=& x - 9, \\
75 x &=& 84x - 756, \\
756 &=& 84x - 75x = 9x, \\
x &=& 84.
\end{aligned}$