Calculating the Number of Sheets of Thick Paper Given Their Weight

Understanding how to calculate the weight of various quantities of paper is a useful skill in many professions, from graphic design to inventory management. This article will walk you through a straightforward problem involving the weight of a specific type of thick paper, helping you to understand the calculation process and conversion between grams and kilograms.

Problem Statement

The problem statement we are dealing with is as follows: If the weight of 15 sheets of thick paper is 50 grams, how many sheets of the same paper would weigh 5/4 kilograms (also known as 1.25 kilograms or 1250 grams)?

Step-by-Step Solution

To solve this problem, we first need to determine the weight of a single sheet of the paper. This can be done by dividing the total weight by the number of sheets:

Weight of each sheet Total weight of 15 sheets / Number of sheets

Plugging in the values:

Weight of each sheet 50 grams / 15 sheets (10 / 3) grams per sheet

Now, we need to determine how many sheets of the same paper would weigh 5/4 kilograms (1250 grams). We know that the weight of x sheets is equal to (10/3) grams per sheet multiplied by x sheets:

(10 / 3) x 1250 grams

Solving for x:

x (10 / 3) [1250 / (10 / 3)] 375 sheets

Verification

Let's verify the solution by calculating the weight of 375 sheets of paper:

First, calculate the weight per sheet (again, for clarity):

Weight per sheet (10 / 3) grams

Now, total weight for 375 sheets:

Total weight (10 / 3) x 375 1250 grams 1.25 kg

This confirms that our calculation is correct and that 375 sheets of the same thick paper would indeed weigh 1.25 kilograms.

Additional Considerations

The problem of converting grams to kilograms is a common task in inventory management and can be applied in various scenarios. For instance, in the paper industry, knowing the weight of a certain number of sheets can help in managing inventory levels and ensuring accurate pricing for products.

When dealing with such problems, it is crucial to ensure that all units of measurement are consistent. In this case, we converted the given weight from grams to kilograms by multiplying by the conversion factor:

1 kilogram 1000 grams

In practice, one should also be cautious about the precision of the measurements used, as even small inaccuracies can result in significant discrepancies when dealing with large quantities of material.

Conclusion

Understanding how to calculate the weight of sheets of paper is a fundamental skill that can be applied in various fields. This article has demonstrated a straightforward method for determining the number of sheets required to achieve a specific weight, converting grams to kilograms, and verifying the accuracy of the calculations.