## 1540.35 – Apples on a Hike

Shannon, Brian, and Dwayne went on a hike and took a bag of apples with them. They stopped for a break for lunch. Shannon, who had been carrying the bag, opened it and and took out $1/3$ of the apples for himself. Brian then took the bag and took out $1/3$ of the remaining apples. Finally, Dwayne took the bag and took out $1/3$ of the apples still remaining. Then they all had lunch. There were $8$ apples left in the sack. How many apples were there originally?

## Solution

Let $x$ represent the number of apples in the bag at the start of the hike.

Shannon eats $\frac{1}{3}x$, with $\frac{2}{3}x$ left.

Brian eats $\frac{1}{3}\cdot \frac{2}{3} x$ or $\frac{2}{9}x$ with $\frac{2}{3} x – \frac{2}{9}x = \frac{4}{9}x$ left.

Dwayne eats $\frac{1}{3}\cdot(\frac{4}{9}x) = \frac{4}{27}x$, with $\frac{4}{9}x – \frac{4}{27}x = \frac{8}{27}x$ left.

We know that $\frac{8}{27}x = 8$ apples, so $x = 27$.

(Shannon ate a lot of apples! But then he's a very big guy.)