A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?
Correct answer: A. 0 < x ≤ 10
- A. 0 < x ≤ 10
- B. 0 < x ≤ 11 (2/3)
- C. 0 < x ≤ 17 (1/2)
- D. 0 < x ≤ 20
Explanation
Choice A is correct because the perimeter of the base is calculated as 7x inches, and the height is 60 inches. By setting up the inequality 7x + 60 ≤ 130 and solving for x, the allowable range for x is 0 < x ≤ 10. This ensures the box dimensions meet the shipping service's restrictions. Choices B, C, and D are incorrect due to miscalculations, misinterpretations, or overlooking key constraints in the problem.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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