Question

Two taxi services charge different rates. Taxi A charges $0.40 permile traveled plus an initial charge of $2.00. Taxi B charges $0.50 permlle traveled. The situation is modeled by this system, where x is thenumber of miles traveled and y is the charge for that distance, incents:y = 40x + 200y = 50xHow many miles must each taxi travel for the charges to be equal,and what is the charge for that distance?O A. Each must travel 10 miles, and the charge is $6.00.O B. The charges will never be equal no matter how far eachtravels.O C. Each must travel 25 miles, and the charge is $12.00D. Each must travel 20 miles, and the charge is $10.00

Answer 1

Given:

The charge in taxi A is $0.40 per mile.

The initial charge in taxi A is $2.00 mile.

The charge in taxi B is $0.50 per mile.

The equation for taxi A is given as y = 40x + 200.

The equation for taxi B is given as y = 50x.

The objective is to find the number of miles (x) each taxi must travel to have equal charges and to find the charge (y).

It is given that x represents the number of miles and y represents the charge for the distance travelled.

Since, the charges are equal, we can equate the given two equations to find the number of miles travelled.

On equating the two equations,

`\begin{gathered} \text{Taxi A = tax}i\text{ B} \\ 40x+200=50x \\ 50x-40x=200 \\ 10x=200 \\ x=(200)/(10) \\ x=20\text{ miles} \end{gathered}`

Now, substitute the value of x in any of the above equation.

Let's take the equation of taxi B.

`\begin{gathered} y=50x \\ y=50(20) \\ y=1000 \end{gathered}`

Since, the equations as given in cents. To convert into dollar, divide the cost by 100,

`\begin{gathered} y=(1000)/(100) \\ y=10\text{ dollars} \end{gathered}`

Thus, to have equal charges for both taxi A and taxi B, the distance required to travel is 20 miles and the charge is $10.

Hence, option (D) is the correct asnwer.