Not Looking for Answers, just don't understand problem.

[abigal09]

I am unable to get ahold of my teacher, and I cannot understand what this problem means:

While 3 Watchmen were guarding an orchard, a theif slipped in and stole some apples. One his way out, he met the 3 Watchmen, one after another, and to
each in turn he gave half of the apples he had and two besides. In this way, he managed to escape with one apple. How many
apples had he stolen originally?

I do not understand what the problem means when it says, "and two besides."

Can anyone help me understand this so I can solve the problem?

 

[mmm4444bot]

… I do not understand … when it says, "and two besides."

The phrase "and two besides" means "plus two more".

EG:

I'm carrying 64 apples, and I meet the first watchman.

Half of 64 is 32.

Plus two more is 34.

I give the first watchman 34 apples.

If I were to try solving this exercise, I think that I would start with the one apple and work backwards.

 

[abigal09]

Here is my answer, is this what you mean?

Watchman 1: 8/2=4+2=6
Watchman 2: 4/2=2+2=4
Watchman 3: 2/2=1+2=3

6+4+3=13

The theif originally stole 13 apples. Does this look right?

(Only I didn't work backwards)

 

[mmm4444bot]

… Watchman 1: 8/2=4+2=6 This shows that the thief stole 8 apples and gave 6 to the first watchman.

After giving away 6 of the 8 apples, the thief is left with 2 apples.

Watchman 2: 4/2=2+2=4 … This shows that the thief had 4 apples, after leaving the first watchman. That's wrong. Your first statement shows that the thief had only 2 apples after leaving the first watchman.

The beginning number of apples when meeting the second watchman has to match the ending number of apples after leaving the first watchman.

The beginning number of apples when meeting the third watchman has to match the ending number of apples after leaving the second watchman.

After giving the third watchman half plus two, the ending number of apples must be 1.

The exercise asks for the number of apples stolen.

Your answer of 8 does not work.

I suggest that you try thinking about how to start with 1 apple and work backwards.

 

[abigal09]

I wasn't sure if I subtracted the additional 2 apples from the total because it looked like it was separate.

1 apple
1x2=2+2=4
4X2=8+2=10
10x2=20+2=22

The total number of apples is 36 then... Does this one look right?

 

[mmm4444bot]

… The total number of apples [stolen] is 36 … Does this one look right?

It's easy to check.

Steal 36 apples.

Meet first watchman, and give away 20 apples (half plus 2).

16 apples left.

Meet second watchman, and give away 10 apples (half plus 2).

6 apples left.

Meet third watchman, and give away 5 apples (half plus 2).

1 apple left.

LOOKS GOOD TO ME!

 

[abigal09]

Thank you SO much for your help!

I psych myself out on some of the easiest problems
sometimes, haha.