Determine the correct numerical value to complete the statement below based on the provide… — Armed Services Vocational Aptitude Battery (ASVAB)

Determine the correct numerical value to complete the statement below based on the provided rates.

Answer:An airborne logistics division drops

3.5

tons of humanitarian rations every

12

minutes. Operating at this constant rate, the division will drop 【52500】 pounds of rations in

1.5

hours.

*(Note:

1 \text{ ton} = 2,000 \text{ pounds}

Answer

52,500

The scenario requires calculating a proportional amount while successfully navigating two unit conversions. First, harmonize the time units by converting

1.5

hours to

90

minutes. Next, convert the initial weight of

3.5

tons into

7,000

pounds. Using these standardized units, set up the proportion:

7,000 \text{ lbs} / 12 \text{ min} = x \text{ lbs} / 90 \text{ min}

. Cross-multiplying gives

12x = 630,000

, and dividing by

12

results in exactly

52,500

pounds.

Step-by-Step Solution

Convert the target time frame from hours to minutes so it matches the time unit in the given rate.

1.5 \text{ hours} \times 60 \text{ minutes/hour} = 90 \text{ minutes}

Direct proportions require time units to be identical across both ratios.

Convert the initial weight from tons to pounds to match the requested unit for the final answer.

3.5 \text{ tons} \times 2,000 \text{ pounds/ton} = 7,000 \text{ pounds}

Harmonizing the weight units prevents conversion errors at the end of the calculation.

Set up a direct proportion equation comparing weight to time.

\frac{7,000 \text{ pounds}}{12 \text{ minutes}} = \frac{x \text{ pounds}}{90 \text{ minutes}}

Because the drop rate is constant, the ratio of weight to time remains equal.

Solve for the unknown weight (x).

x = \frac{7,000 \times 90}{12} = \frac{630,000}{12} = 52,500 \text{ pounds}

Cross-multiplying and dividing isolates the variable, yielding the total pounds dropped over the full time period.

Key Concept

Setting up and solving a direct proportion after performing multiple unit conversions.

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