Optimizing Storage Space for Card Collections: A Mathematical Analysis

When managing a large collection of cards, it is crucial to utilize storage space efficiently. This guide delves into a detailed mathematical analysis to determine the optimal number of card packs that can be stored on a shelf given specific weight and area constraints.

Introduction to the Problem

The initial problem presented involves understanding the dimensions and weight of each card pack and its wrapping paper, as well as the constraint of a shelf with a maximum weight capacity. We begin by breaking down the given data and performing essential calculations to find the maximum number of card packs that can be stored on the shelf.

Given Data and Calculations

Pack Wrapping Weight

Each pack of cards is wrapped in a sheet of 50 grams per square meter (g/m2) paper, with an area of 800 cm2.

The weight of the wrapping paper for each pack is calculated as follows:

Weight of wrapping paper 50 g/m2 x (1 m / 100 cm)2 x 800 cm2 4 grams

Weight of the Card Pack

Each card pack has a total area of 1.5 square meters (m2).

The weight of the cards in the pack is:

Weight of cards 80 g/m2 x 1.5 m2 120 grams

Total Weight of a Wrapped Pack

The total weight of each wrapped card pack is the sum of the paper's weight and the cards' weight:

Total weight of pack 120 grams (cards) 4 grams (wrapping paper) 124 grams

Shelf Capacity

The shelf can hold a maximum of 10 kilograms (kg), which is 10,000 grams.

Number of Card Packs that Can Be Stored

To find the maximum number of card packs that can be stored on the shelf:

Number of packs 10,000 grams / 124 grams/pack 80.64

Since we can only store whole packs, the maximum number of packs is 80.

Verification and Conclusion

The calculations and analysis are based on the given constraints. The weight of the wrapping paper and the cards have been accurately accounted for, ensuring that the maximum number of card packs can be stored without exceeding the shelf's weight capacity.

It is important to note that:

The calculations assume the standard weight and dimensions of a typical card pack. Any variation in the actual weight or dimensions of the cards could affect the final result.

In conclusion, with the given weight and area constraints, the maximum number of wrapped card packs that can be stored on the shelf is 80 packs. By following these calculations, you can optimize your storage space and ensure efficient management of your card collection.

Related Keywords: card storage, weight calculation, packing efficiency