# 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.