Tips & percentages ??

Question

Celeste has $45 that she plans on using to pay for lunch with a friend, including the tip. She always tips 22%. What is the maximum amount Celeste can spend on the food, so she can be sure to have enough money remaining to cover the tip? Round to the nearest cent.

Answer 1

Let x = amount that Celeste will spend on dinner.

The following inequality must be true:

x + 0.22x ≤ 45 (.22x represents amount of the tip, i.e. 22% of x).

1.22 x ≤ 45

x ≤45/1.22 where 45/1.22 ≈ 36.89

So the most Celeste can spend and stay within budget is $36.89.

Check:

22% of 36.89 = 8.1158

36.89 + 8.1158 = 45.0058 (so Celeste cannot round up the tip to 8.12).