16Hit1600
AlgebraVery hardSystem of inequalities for vans and trucks

Algebra practice question

A company must ship at least 200 boxes using vans that carry 30 boxes each and trucks that carry 50 boxes each. It can use at most 6 vehicles in total. Which system of inequalities describes the possible numbers of vans v and trucks t?

  1. A. 30v + 50t ≥ 200 and v + t ≤ 6Correct
  2. B. 30v + 50t ≤ 200 and v + t ≥ 6
  3. C. v + t ≥ 200 and 30v + 50t ≤ 6
  4. D. 30v + 50t ≥ 200 and v + t ≥ 6

Answer: A. 30v + 50t ≥ 200 and v + t ≤ 6

Boxes carried must be at least 200; vehicles used must be at most 6.

Why the other answers are wrong

B. 30v + 50t ≤ 200 and v + t ≥ 6
Both directions are reversed.
C. v + t ≥ 200 and 30v + 50t ≤ 6
The counts and the capacities are swapped.
D. 30v + 50t ≥ 200 and v + t ≥ 6
At most 6 vehicles means v + t ≤ 6.

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