Find out all the meal prices (without tip) between $10.00 and $20.00 inclusive that Dilbert could have ordered so that his total bill with tip is a whole number of dollars (no cents).
COMIC STRIP NO LONGER AVAILABLE.
Solution to the Problem:
There are eleven prices between $10.00 and $20.00 that will yield a whole number when the 15% tip is added:
| Cost of Meal (w/o tip) | Total Price of Meal including Tip | |
|---|---|---|
| $11.30 | $12.995, which rounds to $13.00 | |
| $12.17 | $13.9955, which rounds to $14.00 | |
| $13.04 | $14.996, which rounds to $15.00 | |
| $13.91 | $15.9965, which rounds to $16.00 | |
| $14.78 | $16.997, which rounds to $17.00 | |
| $15.65 | $17.9975, which rounds to $18.00 | |
| $16.52 | $18.998, which rounds to $19.00 | |
| $17.39 | $19.9985, which rounds to $20.00 | |
| $18.26 | $20.999, which rounds to $21.00 | |
| $19.13 | $21.9995, which rounds to $22.00 | |
| $20.00 | $23.00, which rounds to $23.00 |
I thought of two ways to solve this problem:
(1) Write a computer program with a for-loop to find all the values or
(2) Use algebra to solve.
Realizing that a 15% tip added to $10.00 would give $11.50,
the first possible whole number of dollars for the meal and tip would be $12.00.
Let x = cost of the meal alone
Then x + .15 x = 12.00.
Solving for x, we get x = 10.43478...
But when I checked $10.43, I got 11.9945 which rounds to $11.99.
So, I checked $10.44, and I got 12.006 which rounds to $12.01.
So, there was no solution for $12.00.
Then I checked for $13.00.
Solving x + .15x = 13.00,
I got $11.30, which gives 12.995 which rounds to $13.00.
Continue with $14.00, $15.00, ... until you get to $23.00.
Correctly solved by:
| 1. K. Sengupta | Calcutta, INDIA |
| 2. John Funk | Ventura, California |
| 3. Les Walker | Ventura, California |
| 4. Richard K. Johnson | La Jolla, California |