The Problem

Lacey and Ahmed are having lunch. Lacey is paying for lunch, but she has only $24. If she wants to leave a tip, how much can she spend on lunch before the tip?

The Solution

We know that Lacey has $24, but we do not know how what percentage of the total bill she is planning to tip. So, we can look at two cases, both common tip rates. For this investigation, we will see how much money they can spend if Lacey tips 15% and if she tips 20%.


First Case, 15%:

We can write the following equation to determine how much money Lacey and Ahmed can spend. Let m equal the total cost of their meals prior to tip. We can determine the tip amount by multiplying the tip rate by the cost of the food. Thus we have the following equation:

m + 15% * m = $24.00

m + .15m = $24.00

1.15m = $24.00

m = $20.80


Second Case, 20%:

We can use the exact same reasoning to write a new equation, substituting 20% for the 15% from the first case:

m + 20%*m = $24.00

m + .2m = $24.00

1.2m = $24.00

m = $20.00


So, we see that depending on how much she wants to tip, Lacey and Ahmed can spend either $20.80 or $20.00.