Question

A taxi charges a pick-up fee of $2.75 plus a charge per mile. Maria paid $9.00 for a 5-mile ride. Tony paid $12.75 for an 8-mile ride. Write the equation that represents the problem situation where y represents the total cost of a taxi ride after x miles.

Answer 1

The equation representing the total cost of the taxi ride after x miles is y = 2.75 + 1.25x. The equation reflects a $2.75 pick-up fee and a $1.25 per mile charge.

Step-by-step explanation:

The taxi ride pricing problem can be represented by a linear equation where the total cost (y) of the taxi ride is a function of the distance in miles (x). To determine the per-mile charge, we can set up two equations based on the given information: For Maria's 5-mile ride costing $9.00, the equation is 9 = 2.75 + 5c. For Tony's 8-mile ride costing $12.75, the equation is 12.75 = 2.75 + 8c. Here, c represents the charge per mile.

By solving either equation, we find that the charge per mile is c = (9 - 2.75)/5 = $1.25. Therefore, the equation representing the total cost of the taxi ride after x miles is y = 2.75 + 1.25x. The pick-up fee of $2.75 is consistent in both equations, and the charge per mile is the same once calculated.