Question

Yellow Cab Taxi charges a $1.75
flat rate for a ride in the cab. In addition to that, they charge $0.45
per mile. Katie has no more than $12
to spend on a ride. At most, how many miles can Katie travel without exceeding her spending limit?

Answer 1

To determine the maximum number of miles Katie can travel without exceeding her $12 spending limit, we can set up an equation based on the pricing structure of Yellow Cab Taxi.

The total cost \( C \) of a ride is given by:

\[
C = \text{flat rate} + \text{cost per mile} \times \text{number of miles}
\]

According to the problem:

- Flat rate = $1.75
- Cost per mile = $0.45
- Maximum budget = $12

We can express the total cost mathematically as follows:

\[
C = 1.75 + 0.45m
\]

where \( m \) is the number of miles. We want the total cost \( C \) to be less than or equal to $12:

\[
1.75 + 0.45m \leq 12
\]

To isolate \( m \), we first subtract the flat rate from both sides:

\[
0.45m \leq 12 - 1.75
\]
\[
0.45m \leq 10.25
\]

Next, we divide both sides by $0.45:

\[
m \leq \frac{10.25}{0.45}
\]

Calculating the right side:

\[
m \leq 22.7777 \ldots
\]

Since Katie cannot travel a fraction of a mile in this context, we need to round this down to the nearest whole number:

\[
m \leq 22
\]

Therefore, at most, Katie can travel **22 miles** without exceeding her spending limit.