Question

1. A teacher is making gift bags. Each bag is to be filled with pencils and stickers. The reacher has 24 pencils and 36 stickers to use. Each bag will have the same number of each item, with no items left over.

For example, she could make 2 bags with 12 pencils and 18 stickers each.
What are the other possibilities? Explain or show your reasoning.

Answer 1

The teacher can make gift bags in multiple configurations by distributing the 24 pencils and 36 stickers into 1, 2, 3, 4, 6, or 12 bags, all while ensuring each bag contains the same number of items with none left over.

Step-by-step explanation:

The question involves determining the possible ways a teacher can divide 24 pencils and 36 stickers into gift bags, such that each bag has the same number of pencils and stickers with no items left over. To find out how many bags can be made, we need to look for the common factors of 24 and 36.

• The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
• The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Both numbers have the common factors of 1, 2, 3, 4, 6, and 12. So, the teacher can make:

1. 1 bag with 24 pencils and 36 stickers
2. 2 bags with 12 pencils and 18 stickers each
3. 3 bags with 8 pencils and 12 stickers each
4. 4 bags with 6 pencils and 9 stickers each
5. 6 bags with 4 pencils and 6 stickers each
6. 12 bags with 2 pencils and 3 stickers each

Therefore, the other possibilities for number of gift bags are 1,2 , 3, 4, 6, and 12, each containing different quantities of pencils and stickers but always using all the supplies with no leftovers.