Question

City Cab Taxi charges a $2.95
flat rate for a ride in the cab. In addition to that, they charge $0.50
per mile. Katie has no more than $25
to spend on a ride. At most, how many miles can Katie travel without exceeding her spending limit?

Answer 1

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.

1. The flat rate for a ride is $2.95.
2. The charge per mile is $0.50.
3. 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 \( m \):

1. Subtract $2.95 from both sides:

\[
0.50m \leq 25 - 2.95
\]

\[
0.50m \leq 22.05
\]

2. 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**.