Answer to September 6, 2004 Problem |
---|
The Barber Problem |
---|
When I get a haircut, I normally pay my barber with an exact number of dollar bills (which include
the cost of the haircut plus the tip). There are no coins involved in the transaction.
One day, I did not have the exact number of dollar bills, so I gave her a twenty-dollar bill so that she would give me change for the cost of my haircut (which costs less than ten dollars). I would then have enough dollar bills to give her a tip, assuming that she gave me all one-dollar bills. To my surprise, I discovered that my barber thought I was a senior citizen (people 62 or older get one dollar off the regular price of a haircut) because she gave me one dollar too much in change. I was tipping her 37.5% (based on a regular haircut), but how much did my barber think I had been tipping her (based on a senior citizen haircut)? What is the cost of a senior citizen haricut? Extra Credit: How much do you think I will tip my barber next time? |
Solution to the Problem:
My barber thought I was tipping her 57.1% and the cost of a senior citizen haircut is $7.00
(one dollar off the regular price of $8.00).
Let x = the cost of a regular haircut.
|
1. James Alarie |
University of Michigan -- Flint, Flint, Michigan |
2. Josh Feingold | California Institute of Technology Pasadena, California |
3. Tristan Collins | Winchester, Virginia |
4. Ben Schultz | Winchester, Virginia |
5. Jim Arrison | Norristown, Pennsylvania |
6. Jeffrey Gaither | Winchester, Virginia |
7. Tyler Windham | Columbus, Georgia |
8. Joe Jenkins | College of William & Mary Williamsburg, Virginia |
9. Walt Arrison | Philadelphia, Pennsylvania |
10. John Funk | Ventura, California |
11. Julie W. | Dallas, Texas |
12. John Harcourt | Columbus, Georgia |
13. David Amos | Winchester, Virginia |
14. Chris McCormick | Virginia Tech, Blacksburg, Virginia |
15. David & Judy Dixon | Bennettsville, South Carolina |
16. Erik Hultgren | Tullängsskolan, Örebro, Sweden |
17. Jonas Sutinen | Tullängsskolan, Örebro, Sweden |
18. Misty Carlisle | Winchester, Virginia |