Question

Checker Cab Company charges an initial fee of $4.49 and then $1.57 per mile. Yellow Cab Company charges only $2.17 initially, but then $3.72 per mile. Which system of equations can be used to determine the number of miles it takes, x, for the two companies to charge the same amount, y?

a) x = 1.57y + 4.49; x = 3.72y + 2.17
b) y = 1.57x + 4.49; y = 3.72x + 2.17
c) y = 1.57x + 4.49; y = 2.17x + 3.72
d) 1.57x + 4.49y = 6.06; 3.72x + 2.17y = 5.89

Answer 1

The system of equations for Checker Cab and Yellow Cab companies to charge the same amount is y = 1.57x + 4.49 and y = 3.72x + 2.17, which is option b).

Step-by-step explanation:

The correct system of equations to determine the number of miles (x) it takes for Checker Cab Company and Yellow Cab Company to charge the same amount (y) is given by option b):

y = 1.57x + 4.49;
y = 3.72x + 2.17

These equations represent the total cost (y) as a function of the number of miles (x). The first equation represents Checker Cab Company with its initial fee of $4.49 and the cost per mile of $1.57. The second equation represents Yellow Cab Company with an initial fee of $2.17 and the cost per mile of $3.72. To find the number of miles where the total cost is the same for both companies, we would set the two equations equal to each other and solve for x.