Question

Use the image to help you answer Parts A and B.

Part A

Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included.

If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of
different arrays.

Answer 1

To determine how many different arrays can be formed with 24 eggs, we need to find all the unique pairs of factors that multiply together to equal 24. We can do this by finding the factor pairs:

1. 1 × 24
2. 2 × 12
3. 3 × 8
4. 4 × 6

Now, we will consider each of these pairs as arrays where the order does not matter:

- 1 × 24
- 2 × 12
- 3 × 8
- 4 × 6

Since arrays are equivalent when the order of dimensions is switched (e.g., 3 × 8 is the same as 8 × 3), we only count the unique arrangements in increasing order by their factors.

Thus, the unique arrays that can be formed with 24 eggs are:
1. 1 × 24
2. 2 × 12
3. 3 × 8
4. 4 × 6

Adding these together, we find that we have a total of **4 different arrays** to package the 24 eggs.

**Answer: 4 different arrays.**