Word Problem (finding original amount of candy)

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reinisch

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A child has a bag of candy. A bully takes 1/2 the candy plus two. Another bully takes 1/2 of what is left plus two. A third bully takes 1/2 of what is left plus two. How much candy was there initially if all that is left is 2?

I know that part of the equation is: 1/2x+2. If I repeat this three times, I get something like 1/8x+6.

Could you please help me "see" what I can't see?

Thanks,

Laura
 
Re: Word Problem

The equation to produce the answer seems to me to be a little too complex for pre-algebra. If you must have an equation--- I'll try to get you started.
Let x be the original number of candies.
The first bully took half of them plus 2. That would be (1/2)x+2. Now, how many are left?
x - [(1/2)x+2] = x- (1/2)x - 2 = (1/2)x - 2 <--- That's how many are left.
The next bully takes half of those plus 2. To get the number that are left we have...
[(1/2)x-2] - (1/2)[(1/2)x-2] - 2. <--- That's how many are left after the 2nd bully does his thing.
I leave the rest to you.

You might consider working from the end back toward the beginning.
If she has two left, then the 3rd bully had taken 2 + half of the preceding amount. So 4 is half of the preceding amount meaning there were 8 pieces before the third bully took what he took. In like manner you can take the next two steps. Again, I don't want to take the pleasure of solving this away from you. For the answer that I got, you might highlight between the asterisks. *44*
 
Re: Word Problem

A child has a bag of candy. A bully takes 1/2 the candy plus two. Another bully takes 1/2 of what is left plus two. A third bully takes 1/2 of what is left plus two. How much candy was there initially if all that is left is 2?
Click to expand...
Work backwards.

There are 2 left.
Add back the "plus 2" that the 3rd bully takes making 4.
This represents what was left after the 3rd bully took 1/2 making 8 left after the 2nd bully finished.
Add back the "plus" 2 that the 2nd bully takes making 10.
This represents what was left after the 2nd bully took 1/2 making 20 left after the 1st bully finished.

I'll let you take it to its conclusion by following the same steps that we just went through.
 
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