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.