Question

The man entered an orchard that had 7 guards and picked some apples. When he left, he gave the first guard half his apples and 1 apple more. To the second guard, he gave half his remaining apples and 1 more. He did the same to each of the remaining five guards and left the orchard with 1 apple. How many apples did he gather in all? Explain how you solved the problem.

Answer 1

896 apples

Explanation:

We need to order this data to solve the problem. "X" will be the total number of apples he collected.

"He gave the first guard half of his apples and 1 apple more". Mathematically:

`Guard 1 = (X)/(2)+1\\`

"To the second guard, he gave half his remaining apples and 1 more". Mathematically:

`Guard2 = (X)/(4)+1`

"He did the same to each of the remaining five guards". Mathematically:

`Guard3to7 = (X)/(8)+1+(X)/(16)+1+(X)/(32)+1+(X)/(64)+1+(X)/(128)+1`

Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":

`X= (X)/(2)+1 + (X)/(4)+1 + (X)/(8)+1+(X)/(16)+1+(X)/(32)+1+(X)/(64)+1+(X)/(128)+1`

Solving this equation results in X = 896 apples.