Expert: Abe Mantell - 5/27/2005

Question
I have a word problem I can't figure out...
hank had to give a guard 1/3 of his coins to leave town. in order to get on the highway he had to give a guard 1/2 of his coins. to pay for gas he had to use 1/4 of his coins. to buy dinner he used 2/3 of his coins. at this point he had 7 coins left.
I have an idea how to solve this problem, but I just can't figure it out. I would really appreciate the help! Thanks so much.

Answer
I gather you mean that at each stage he gave that fraction
of money he had left...yes?  If so, then here is a solution:

Let x=the original number of coins.
After giving 1/3 of it, he had (2/3)x left.
Then he gave 1/2 of that, leaving (1/2)(2/3)x=(1/3)x
Then he gave 1/4 of that, leaving (3/4)(1/3)x=(1/4)x
Then he used 2/3 of that, leaving (1/3)(1/4)x=(1/12)x
So, (1/12)x=7...thus, x=12*7=84 coins.

OK?

Abe