Math problem

[Ed62]

Here's one I saw in a magazine today. See if you can figure it out. No prizes, but you get bragging rights.

A man had a basket full of apples. He saw a little girl, and gave her half the apples, plus another half apple. A short while later, he saw another little girl. He gave her half of those left in the basket, plus another half apple. Finally he saw yet another little girl, and he gave her half of what was left, plus another half apple. His basket was now empty. How many apples were initially in the basket?

Ed

[big tim]

I come up with 6

Tim

[Ed62]

Sorry, no cigar.

Ed

[drumpriest]

I believe 7 is correct.

[TheRic]

I believe 7 is correct.

I'll second that

[Ed62]

You are correct! You get bragging rights.

Ed

[drumpriest]

Woot! brag brag brag........I sense that noone cares. :-D

[p8ntblr]

Kinda late.. but I came up with 7 as well. Did you guys work it backwards as well?

[Greg in Maryland]

Ok, I'll risk public humiliation and and say I don't get the solution, or perhaps the problem.

Girl 1 gets 1/2 of the basket of apples and 1/2 of a single apple

Girl 2 gets 1/2 of the remaining apples and 1/2 of a single apple

Girl 3 gets 1/2 of the remaining apples and 1/2 of a single apple

and there are no apples left at the end of the day.

What happened to the remaining 1/2 of an apple? The problem does does not state that each girl receives a diminishing portion of the fractional apple. It states: "plus another half apple" not "plus half of the remaining half apple" or "half of the half apple." I don't see how this works.

Can someone explain 3rd grade algebra to me? My brain isn't working to well tonight.

Greg

[drumpriest]

p8ntblr, yeah, I worked it backwards, the key is realizing that when girl #3 arrives, he has 1 apple in the basket.

If he gives 1/2 of his apples to the girl + 1/2 apple, and has nothing left, he must have started with 1.

1 divided by 2 = 1/2 + 1/2

From there it's trivial to figure the rest of it.

working from the front...

7 / 2 = 3.5 - 0.5 = 3.0
3.0 / 2 = 1.5 - 0.5 = 1.0
1.0 / 2 = 0.5 - 0.5 = 0

[p8ntblr]

EDIT : What drumpriest said

[LCHIEN]

see that's not right. If there were intially 7 apples, and the first girl got half of them plus 1/2 of an apple then she should have had 4. Half the apples were 3.5 apples, plus another half makes 4.

It was obvious to me if he was giving half apples, then when we were talking half of what he had he would have been willing to split them when dealing with half an odd number...

[drumpriest]

Yeah Loring, the first girl does get 4 apples. I should have written that better.

First Girl:
7 - (7/2 + 0.5) = 3
Second Girl:
3 - (3/2 + 0.5) = 1
Third Girl:
1 - (1/2 + 0.5) = 0

[LCHIEN]

oh, OK.....

[sacherjj]

I'm in late, but didn't scroll down until I finished it.

A = # of apples at start.
Girl1 = A/2 + 1/2
Girl2 = (A/2 - 1/2)/2 + 1/2
Girl3 = ((A/2 - 1/2)/2 - 1/2)/2 + 1/2

Girl3 = 1 apple, because she received 2 x 1/2 apple.

Solve for A
1 = ((A/2 - 1/2)/2 - 1/2)/2 + 1/2
1/2 = (A/4 - 1/4 - 1/2)/2
1/2 = A/8 - 1/8 - 1/4
4/8 + 1/8 + 2/8 = a/8
7/8 = A/8
A = 7

7 apples.

Girl 1 got 4 apples
Girl 2 got 2 apples
Girl 3 got 1 apple.