1540.35 – Apples on a Hike

Tags:Problem Set 3Pre-Calculus MathAlgebra

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 1/31/3 of the apples for himself. Brian then took the bag and took out 1/31/3 of the remaining apples. Finally, Dwayne took the bag and took out 1/31/3 of the apples still remaining. Then they all had lunch. There were 88 apples left in the sack. How many apples were there originally?


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

Shannon eats 13x\frac{1}{3}x, with 23x\frac{2}{3}x left.

Brian eats 1323x\frac{1}{3}\cdot \frac{2}{3} x or 29x\frac{2}{9}x with 23x29x=49x\frac{2}{3} x – \frac{2}{9}x = \frac{4}{9}x left.

Dwayne eats 13(49x)=427x\frac{1}{3}\cdot(\frac{4}{9}x) = \frac{4}{27}x, with 49x427x=827x\frac{4}{9}x – \frac{4}{27}x = \frac{8}{27}x left.

We know that 827x=8\frac{8}{27}x = 8 apples, so x=27x = 27.

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