September 2013
Problem of the Month

Tipping Problem

Mr. P follows this rule when tipping at restaurants:
He figures 20% of the bill (food plus tax), and then he rounds up to the nearest dollar.

If Mr. P tips $8.00, what is the total amount of his bill (food plus tax plus tip)?

Give the entire range of values that work.

Solution to the Problem:

The total amount of the bill could be any amount from $43.01 to $48.00 inclusive.

Let x = cost of the food plus tax.
Then solve .20 x = 8.00 to get x = $40.00.
Then solve .20 x = 7.00 to get x = $35.00.
So, the values of x that result in a tip of $8.00 would be any amount over $35.00 and less than or equal to $40.00.
Then add the $8.00 tip to the values of x to get the total.

Correctly solved by:

1. William Vargo	Calgary, Alberta, Canada
2. James Alarie	Flint, Michigan

Send any comments or questions to: David Pleacher