Final answer:
To find the difference between the cost of the taxi ride and the limo ride, we need to calculate the cost of each ride. The cost of the taxi ride is calculated based on the number of additional quarter miles traveled, while the cost of the limo ride is calculated based on the number of miles traveled. After calculating the costs, we can find the difference.
Step-by-step explanation:
To calculate the cost of the taxi ride, we need to find the number of additional quarter miles traveled. Let's assume the salesman traveled x number of additional quarter miles. The total cost of the taxi ride is given as $30.75. The cost for the first quarter-mile is $1.50, and the cost for each additional quarter mile is $0.75. So, the equation to calculate the total cost is: $1.50 + ($0.75 * x) = $30.75. Solving this equation, we find that x = 36. Hence, the salesman traveled 36 additional quarter miles.
Now, let's calculate the cost of the limo ride. The limo driver charges $2.50 per mile. To find the number of miles traveled, we need to convert the additional quarter miles traveled by the salesman to miles. Since 1 mile is equal to 4 quarter miles, the number of miles traveled by the salesman is x/4. Hence, the cost of the limo ride is: $2.50 * (x/4) = $2.50 * (36/4) = $9.00.
The difference between the cost of the two rides is: $30.75 - $9.00 = $21.75. Therefore, the answer is $21.75 (rounded to the nearest cent).