Final answer:
The correct system of equations for determining when Checker Cab and Yellow Cab have the same charge is y = 1.41x + 4.88 for Checker Cab and y = 3.67x + 2.94 for Yellow Cab. These two equations allow us to solve for x, the number of miles where both cabs charge the same amount. None of the provided options match this system correctly.
Step-by-step explanation:
To determine the number of miles it takes, x, for Checker Cab Company and Yellow Cab Company to charge the same amount, y, we need to set up two equations that represent each company's charging system. For Checker Cab Company, the equation will include their initial fee of $4.88 and their per-mile charge of $1.41. For Yellow Cab Company, the equation will include their initial fee of $2.94 and their per-mile charge of $3.67.
The correct system of equations should represent the total charge, y, as a function of the number of miles, x. Therefore, the system of equations is:
- Checker Cab Company: y = 1.41x + 4.88
- Yellow Cab Company: y = 3.67x + 2.94
We are looking for the point where the two companies charge the same amount, so the equations for y should be set equal to each other:
- 1.41x + 4.88 = 3.67x + 2.94
None of the options provided perfectly match the system of equations we are looking for. However, we are looking for a pair of equations that can be used to calculate when Checker Cab and Yellow Cab charge the same, so the closest option to what we need seems to be missing in the provided list.