4
algebra

A ride-sharing service charges $3.50 per mile plus a $5 base fare. If a passenger has at most $40, which inequality represents the maximum miles mm they can travel?

A

3.50m+5≤403.50m + 5 \leq 40

B

3.50m+5≥403.50m + 5 \geq 40

C

5m+3.50≤405m + 3.50 \leq 40

D

3.50m−5≤403.50m - 5 \leq 40

Correct Answer: A

Choice A is the correct answer. Setting up inequalities from word problems requires identifying variable costs and constraints.

  1. Identify costs: $3.50 per mile means 3.50m3.50m, base fare is $5
  2. Total cost: 3.50m+53.50m + 5
  3. Constraint: "At most $40" means ≤40\leq 40
  4. Result: 3.50m+5≤403.50m + 5 \leq 40

?�� Strategic Tip: "At most" indicates a maximum limit, translating to ≤\leq in inequality notation.

Choice B is incorrect because≥40\geq 40 means spending at least $40, contradicting the "at most" constraint. Choice C is incorrect because it reverses the per-mile cost and base fare, making the base fare vary with miles. Choice D is incorrect because it subtracts the base fare instead of adding it, which doesn't match the pricing structure.

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Linear Functions Set 62