To find out how many miles Katie can travel without exceeding her spending limit, we can set up the following inequality based on the information provided.
- The flat rate for a ride is $2.95.
- The charge per mile is $0.50.
- Katie's total budget is $25.
We can express the total cost \( C \) of the ride as:
\[ C = 2.95 + 0.50 \times m \]
where \( m \) is the number of miles traveled. We need this total cost to be less than or equal to $25:
\[ 2.95 + 0.50m \leq 25 \]
Now, we will isolate \( m \):
- Subtract $2.95 from both sides:
\[ 0.50m \leq 25 - 2.95 \]
\[ 0.50m \leq 22.05 \]
- Now, divide both sides by $0.50:
\[ m \leq \frac{22.05}{0.50} \]
\[ m \leq 44.1 \]
Since Katie cannot travel a fractional mile in this context, we round down to the nearest whole number. Therefore, the maximum number of miles Katie can travel is:
\[ m = 44 \]
Thus, the most miles Katie can travel without exceeding her spending limit is 44 miles.
3 answers