Packing 15 Pastries and 12 Biscuit Packets into Identical Boxes

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: 15 pastries and 12 biscuit packets have been donated for a school fete. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries will each box contain?

Step 1: Identify the Mathematical Concept

The maximum number of identical boxes that can be made is given by the HCF (Highest Common Factor) of 15 and 12.

Step 2: Find the HCF of 15 and 12

Using Euclid’s division algorithm:

15 = 12 × 1 + 3

12 = 3 × 4 + 0

Since the remainder is zero,

∴ HCF (15, 12) = 3

Step 3: Find the Contents of Each Box

Number of boxes = 3

Pastries in each box = 15 ÷ 3 = 5

Biscuit packets in each box = 12 ÷ 3 = 4

Final Answer

∴ Each box will contain 5 pastries and 4 biscuit packets.

Conclusion

Thus, by using the HCF of 15 and 12, we find that the donated items can be packed into identical boxes each containing 5 pastries and 4 biscuit packets.