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.
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