AlgebraMediumChoosing the inequality for a minimum with a fixed cost
Algebra practice question
A charity run costs $250 to organise. Each runner pays a $15 entry fee. Which inequality gives the numbers of runners n for which the run raises at least $500 after costs?
- A. 15n − 250 ≥ 500Correct
- B. 15n − 250 ≤ 500
- C. 15n ≥ 500
- D. 15n + 250 ≥ 500
Answer: A. 15n − 250 ≥ 500
Money raised after costs is 15n − 250, and 'at least 500' is ≥ 500. (This gives n ≥ 50.)
Why the other answers are wrong
- B. 15n − 250 ≤ 500
- ≤ would cap the amount raised.
- C. 15n ≥ 500
- Ignores the $250 cost.
- D. 15n + 250 ≥ 500
- Adds the cost instead of subtracting it.
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