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

x12+x6+x7+5+x2+4=x,7x84+14x84+12x84+5+42x84+4=x,75x84+9=x,75x84=x−9,75x=84x−756,756=84x−75x=9x,x=84. \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}