Lindy's Taxi charges a fee of 1.50 per mile
The Correct Answer and Explanation is:
The correct answer is 30 miles.
To determine the number of miles at which the cost for both taxi companies is the same, we can set up an algebraic equation for each company’s pricing structure. Let ‘m’ represent the number of miles traveled.
First, we will formulate the cost equation for Lindy’s Taxi. The company charges a fixed fee of $25 plus $1.50 for every mile. The total cost for a ride with Lindy’s Taxi can be expressed as:
Cost for Lindy’s = 25 + 1.50m
Next, we will create the cost equation for Checker Taxi. This company has a fixed fee of $40 plus $1.00 for every mile. The total cost for a ride with Checker Taxi is represented by the equation:
Cost for Checker = 40 + 1.00m
The problem asks for the point where the costs are equal. To find this, we set the two equations equal to each other:
25 + 1.50m = 40 + 1.00m
Now, we need to solve this equation for ‘m’. We can begin by consolidating the terms with ‘m’ on one side of the equation. By subtracting 1.00m from both sides, we get:
25 + 0.50m = 40
Next, we isolate the term containing ‘m’ by moving the constant numbers to the other side. We can subtract 25 from both sides of the equation:
0.50m = 40 – 25
0.50m = 15
Finally, to solve for ‘m’, we divide both sides by 0.50:
m = 15 / 0.50
m = 30
Thus, at 30 miles, the cost for both taxi companies will be identical. We can verify this by calculating the total cost for each company at 30 miles.
For Lindy’s Taxi:
25+(25+(1.50 × 30) = $25 + $45 = $70.
For Checker Taxi:
40+(40+(1.00 × 30) = $40 + $30 = $70.
Since both totals are $70, the answer of 30 miles is correct.
