Question

Aimee has 20 apples and wants to have the same amount of apples in each bag but ends up with more than one bag of apples and each bag to contain more than one apple

work out all the possibilities for all of the number of apples that she could use for each bag

Answer 1

• There are 4 possibilities: 2, 4, 5 or 10 apples in each bag.

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Let the number of apples in each bag is x, then the number of bags is 20/x.

Since the number of apples in each bag is greater than one and number of bags is greater than one, we have the following conditions:

• x > 1 ,
• 20/x > 1 ⇒ x < 20,
• x is factor of 20.

The factors of 20 between 1 and 20 are:

• 2, 4, 5, 10

The possibilities are:

1. If x = 2, then the number of bags is 20/2 = 10;
2. If x = 4, then the number of bags is 20/4 = 5;
3. If x = 5, then the number of bags is 20/5 = 4;
4. If x = 10, then the number of bags is 20/10 = 2.