AlgebraVery hardFeasible distances under a budget and a minimum
Algebra practice question
A van hire costs $25 per day plus $0.40 per kilometre. A courier hires the van for 3 days, must drive at least 200 kilometres, and can spend at most $200. Which inequality describes all possible numbers of kilometres m the courier can drive?
- A. 200 ≤ m ≤ 312.5Correct
- B. m ≤ 312.5
- C. 200 ≤ m ≤ 500
- D. m ≥ 200
Answer: A. 200 ≤ m ≤ 312.5
Cost: 75 + 0.4m ≤ 200 → m ≤ 312.5. With the minimum: 200 ≤ m ≤ 312.5.
Why the other answers are wrong
- B. m ≤ 312.5
- Omits the 200-kilometre minimum.
- C. 200 ≤ m ≤ 500
- 500 comes from 200 ÷ 0.4, ignoring the daily charges.
- D. m ≥ 200
- Omits the budget limit.
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