This year my teacher read us the book The Phantom Tollbooth, and since then I've been having strange dreams about drving in usuaual places and paying tolls unusual characters.Last night I dreamed about highway in the clouds near the mythical Mt. Olympus. At my first tollbooth a mythical goddess asked for one-half my gold pieces plus two more. At the next tollbooth,a Greek hero demanded one-half my remaining gold pieces plus two more. Then at third booth,Zenus himself asked me for one-half my remaining gold pieces plus two more.As I approaches another toolbooth I began to worry that I wouldn't have enough gold pieces for all the tollbooths. I wondered what they did to people without enough gold pieces. I looked im my purse and nocited I only had four pieces left. I was really beginning to worry, when my mom woke me up by calling me to breakfast. How many gold pieces did I start with in this dream?

Question

Thanks very much!

Answer 1

You ended up with 4 gold pieces.

Zenus asked you for 1/2 your gold + 2. So you lost 1/2 of your gold and then 2 more.

First add 2 to 4, yielding 6. Now divide by 1/2, or multiply by 2, which yields 12.

Now, try to work out the other 2 "toll booths" in the same fashion to determine the gold at the start.