Question

vijay needs to take a taxi, which costs a flat fee of 3 dollars, plus an additional 4 dollars per mile. if vijay has ( a ) dollars with him, which inequality shows the number of miles, ( m ), he can afford to travel in the taxi?

choose 1 answer:

a ( 0 leq m leq 4a - 3 )

b ( 0 leq m leq \frac{a}{4} - \frac{3}{4} )

c ( 4a - 3 leq m )

d ( \frac{a}{4} - \frac{3}{4} leq m )

Explanation:

Step1: Define total cost formula

Total cost = Flat fee + Mileage cost: $3 + 4m$

Step2: Set up affordability inequality

Total cost ≤ money Vijay has: $3 + 4m \leq a$

Step3: Isolate m (subtract 3)

$4m \leq a - 3$

Step4: Solve for m (divide by 4)

$m \leq \frac{a}{4} - \frac{3}{4}$

Step5: Add non-negative mile constraint

Miles can't be negative: $0 \leq m$

Answer:

B. $0 \leq m \leq \frac{a}{4} - \frac{3}{4}$