To determine how many miles Katie can travel without exceeding her spending limit of $20, we first calculate how much she has left after paying the flat rate of $4.95.
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Subtract the flat rate from her total budget: \[ 20 - 4.95 = 15.05 \] So, Katie has $15.05 available to spend on mileage.
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The cost per mile is $0.49. To find out how many miles she can travel for $15.05, we divide the available amount by the cost per mile: \[ \text{Number of miles} = \frac{15.05}{0.49} \]
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Now, calculate the number of miles: \[ \text{Number of miles} \approx 30.6122449 \] Since Katie can't travel a fraction of a mile, we will round down to the nearest whole number: \[ \text{Number of miles} = 30 \]
Therefore, at most, Katie can travel 30 miles without exceeding her spending limit of $20.