Question

4

A taxicab fare starts with a base charge. Then an additional
amount is added for each mile. The system of equations
shows the fares for two different cab companies.
Cab company A: y = 3 +2.25x
Cab company B: y = 2 + 3.50x
a. What do x and y represent in each equation?
b. Solve the system to find x and y. What does the solution
tell you about the two cab companies?

Answer 1

a.) In both equations, the variable “x” is equal to the miles traveled. The variable “y” is equal to the total fare after “x” miles.

b.) solving via substitution method:

(3+2.25x)=(2+3.50x)

Solve for x:

Subtract 2 from both sides:

3-2+2.25x=3.50x

1+2.25x=3.50x

Subtract 2.25x from both sides:

1=1.25x

Divide both sides by 1.25x

x=.8

Now, substitute “x” in for one of the equations to solve for “y:”

y=3+2.25(.8)

y=3+1.8

y=4.8

Thus, the solution is: (.8, 4.8)

This solution tells us that the fares will cost the same (y) when the miles traveled (x) equal .8 miles. So, the two fares cost $4.8 each after .8 miles.