Question

two ride - sharing companies charge customers a base fare and then an additional fee per mile.

• ridearound charges a base fare of $5 and $1.50 per mile.
• cargo charges a base fare of $10 and $0.75 per mile.

let x represent the number of miles and let y represent the total cost, in dollars. which of the following systems of equations best represents this situation?
\\(\

$$\begin{cases}y = 6.5x\\\\y = 10.75x\\end{cases}$$

\\)
\\(\

$$\begin{cases}5y = 1.5x\\\\10y = 0.75x\\end{cases}$$

\\)
\\(\

$$\begin{cases}y = 5x + 1.5\\\\y = 10x + 0.75\\end{cases}$$

\\)
\\(\

$$\begin{cases}y = 1.5x + 5\\\\y = 0.75x + 10\\end{cases}$$

\\)

Explanation:

Step1: Analyze RideAround's cost

RideAround has a base fare of $5 and $1.50 per mile. The total cost \( y \) is base fare plus (cost per mile times number of miles \( x \)). So the equation is \( y = 1.5x + 5 \).

Step2: Analyze CarGo's cost

CarGo has a base fare of $10 and $0.75 per mile. Using the same total cost formula, the equation is \( y = 0.75x + 10 \).

Answer:

\( y = 1.5x + 5 \) and \( y = 0.75x + 10 \) (the last option: \( y = 1.5x + 5 \); \( y = 0.75x + 10 \))