Question

City Cab Company charges $3.00 per ride plus $2.00 per mile traveled. Metro Cab Company charges $1.50 per ride plus $2.50 per mile traveled. Write an equation to find m, the number of miles for which the total cost is the same for both taxi companies. Then solve the equation to find the number of miles when the cost is the same, and state what that cost is.

Answer 1

$9

Explanation:

Let's start by writing the equations for the total cost of each company. For City Cab Company, the total cost (C) is given by:

C = 3 + 2m

where m is the number of miles traveled.

For Metro Cab Company, the total cost (M) is given by:

M = 1.5 + 2.5m

To find the number of miles for which the total cost is the same for both taxi companies, we need to set C equal to M and solve for m:

3 + 2m = 1.5 + 2.5m

0.5m = 1.5

m = 3

Therefore, the cost will be the same for both taxi companies when the number of miles traveled is 3. To find the cost, we can substitute m = 3 into either equation. Let's use the City Cab Company equation:

C = 3 + 2(3) = 9

So the cost for both taxi companies will be the same when 3 miles are traveled, and the cost will be $9.

Answer 2

Let's assume that x represents the number of miles traveled.

For City Cab Company, the total cost would be the sum of the initial ride charge and the charge per mile:

Total Cost for City Cab = 3.00 + 2.00x

For Metro Cab Company, the total cost would be:

Total Cost for Metro Cab = 1.50 + 2.50x

To find the number of miles, m, for which the total cost is the same for both taxi companies, we can set the two expressions equal to each other and solve for x:

3.00 + 2.00x = 1.50 + 2.50x

Subtracting 2.00x from both sides, we get:

3.00 = 1.50 + 0.50x

Subtracting 1.50 from both sides, we get:

1.50 = 0.50x

Dividing both sides by 0.50, we get:

x = 3

So the number of miles for which the total cost is the same for both taxi companies is 3 miles.

To find the cost for this distance, we can plug x = 3 into either of the expressions for the total cost. For example, using the expression for City Cab Company:

Total Cost = 3.00 + 2.00(3) = 9.00

Therefore, the cost for traveling 3 miles is $9.00 for both taxi companies.