Verified Answer :

  • Understand the conversion: \(1 \text{ ton} = 2,000 \text{ pounds}\).
  • Convert \(10 \text{ tons}\) to pounds: \(10 \times 2,000 = 20,000 \text{ pounds}\).
  • Compare the values: \(20,002 \text{ pounds} > 20,000 \text{ pounds}\).
  • Identify the greater value: \(\boxed{\text{a. } 20,002 \text{ pounds}}\).

Explanation

  1. Analysis of the Problem and Data

We are tasked with comparing two weights: \(20,002\) pounds and \(10\) tons. To determine which is greater, we must express both quantities in the same unit. We use the standard conversion factor for the United States customary system, which states that one ton is equivalent to two thousand pounds:
\[1 \text{ ton} = 2,000 \text{ pounds}\]

  1. Converting Tons to Pounds

Now, we convert the \(10\) tons measurement into pounds by multiplying by the conversion factor:
\[10 \text{ tons} \times 2,000 \frac{\text{pounds}}{\text{ton}} = 20,000 \text{ pounds}\]
This calculation shows that \(10\) tons is exactly \(20,000\) pounds.

  1. Comparison and Conclusion

Finally, we compare the two values in pounds: \(20,002\) pounds and \(20,000\) pounds. Since \(20,002 > 20,000\), it follows that \(20,002\) pounds is heavier than \(10\) tons. Therefore, option (a) is the correct choice.
\(\boxed{\text{a. } 20,002 \text{ pounds}}\)

Examples

In logistics and freight transportation, weight units must be carefully converted. For example, a cargo ship may have a weight capacity listed in tons, while the individual containers are weighed in pounds. Knowing these conversions allows dock workers to ensure that the total weight of the containers does not exceed the vessel's capacity, preventing dangerous overload conditions. Comparing weights accurately is a fundamental skill for logistics safety and efficiency.

Related Questions