SOLUTION: Four children find a magic token that grants half of any wish. Their mother takes the token with her to a destination 20 miles away, and when she wishes she was home, she magicall

Question 38580: Four children find a magic token that grants half of any wish. Their mother takes the token with her to a destination 20 miles away, and when she wishes she was home, she magically ends up halfway home. If the mother continues to make the same wish, how many more wishes will it take for her to be within 100 feet of her house?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
She begins the problem at a distance of 10 miles from home, having already used one wish to get halfway home. The question is "how many MORE wishes will get her within 100 feet of home?" She is starting out at 10 miles = 52800 feet, and she divides by 2 each time she makes a wish. Let's say that it takes n wishes. The equation at which she will be 100 feet from home is this:

To solve this, multiply both sides of the equation by .

Divide both sides by 100:

Notice that 2^9 = 512, so if n= 9 wishes, her distance from home is feet. This is NOT QUITE enough, so she will have to make ONE more wish, which will be a total of 10 "more" wishes to get within 100 feet.

Does that look right? I'm sure mathematicians have a much more formal explanation, but I hope this will be easier to understand.

R^2 at SCC

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