How many apples were picked?

Question

Mark, Juan, David and Hua spent the afternoon picking apples, which they put into a large box. They were so tired from their labors that they went to sleep early that evening. During the night, Mark awoke, took ¼ of the apples from the box, put them into his pack, and went back to sleep. Later, Juan awoke, took ¼ of the apples from the box, put them into his pack, & went back to sleep. Later, Hua awoke, took ¼ of the apples in the box, & put them into his pack. He, too, went back to sleep. Finally, just before daylight, David awoke took ¼ of the apples from the box, put them into his pack, & woke the other three boys. They counted the apples & found 81 apples in the box. How many apples had they picked?

Answer 1

Let x = number total of apples picked and initially placed in the box.

 

Number left after Mark:  x - x/4 = (3/4) x

Number left after Juan:  (3/4) x - (3/4) x/4 = (3/4)^2 x

Number left after Hua:   (3/4)^2 x - (3/4)^2 x/4 = (3/4)^3 x

Number left after David:  (3/4)^3 x - (3/4)^3 x/4 = (3/4)^4 x

 

The number left after David = 81

 

81 = (3/4)^4 x

 

x = 81 / (3/4)^4 = 256

 

There were 256 apples in the box to begin with, so they picked 256 apples.