AlgebraEasyInterpreting a linear inequality to find a minimum count
Algebra practice question
During a practice session, a rowing team has already rowed 1,200 meters as a warm-up. Each timed interval after the warm-up covers 500 meters. The coach requires the team to row a total of at least 6,000 meters in the session.
What is the least number of timed intervals the team must complete to meet the coach's requirement?
- A. 9
- B. 10Correct
- C. 12
- D. 14
Answer: B. 10
If r is the number of intervals, then 500r + 1200 ≥ 6000, so 500r ≥ 4800 and r ≥ 9.6. Since r must be a whole number, the least value is 10. Choice A rounds 9.6 down; 9 intervals give only 1,200 + 4,500 = 5,700 meters, which is short of 6,000. Choice C ignores the 1,200-meter warm-up and computes 6000 ÷ 500 = 12. Choice D adds the warm-up instead of subtracting it, computing (6000 + 1200) ÷ 500 = 14.4 and then truncating.
Why the other answers are wrong
- A. 9
- You got r ≥ 9.6 correctly but rounded down; 9 intervals give only 1,200 + 4,500 = 5,700 meters, short of the 6,000 required, so you must round up to 10.
- C. 12
- You computed 6000 ÷ 500 = 12, forgetting that the 1,200-meter warm-up already counts toward the total. Subtract it first: 4800 ÷ 500 = 9.6, so 10 intervals.
- D. 14
- You added the warm-up instead of subtracting it: (6000 + 1200) ÷ 500 = 14.4. The 1,200 meters are already rowed, so use (6000 − 1200) ÷ 500 = 9.6 and round up to 10.
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