Answer:
896 apples
Step-by-step 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:
[tex]Guard 1 = \frac{X}{2}+1\\[/tex]
"To the second guard, he gave half his remaining apples and 1 more". Mathematically:
[tex]Guard2 = \frac{X}{4}+1[/tex]
"He did the same to each of the remaining five guards". Mathematically:
[tex]Guard3to7 = \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]
Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":
[tex]X= \frac{X}{2}+1 + \frac{X}{4}+1 + \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]
Solving this equation results in X = 896 apples.
