How many apples are there in a string bag if there are more than 11 apples in a string bag? Find all possible?
Let us say box contain x number of apple, bag contain y number of apple and string bag contain z number of apple.
In first day shop keeper receives (9x+3y) apples.
When he repacks he use 11 string bags. At that time he had less than 97 apples left without packing in string bags.
[Apples received > apples in string bags +97]
Because we have less than 97 apples left.
9x+3y > 11z+97------(1)
On second day he receives (6x+2y) apples.
When he repack he use 8 string bags. At that time he had lat least 56 apples left without packing in string bags.
[Apples received >= apples in string bags +56]
Because we have at least 56 apples left.
6x+2y >= 8z+56
We can divide this by 2.
3x+2y >= 4z+28------(2)
9x+3y >= 12z+84------(3)
Now we have two expressions for (9x+3y). (1) is absolutely greater than (9x+3y) but (3) is greater than or equal to (9x+3y).
So we can be sure that (1)>=(3)
13 >= z
So in each string bag we can have apples less than or equal to 13. It is given that a string bag contains more than 11 apples.
So z = 12 or z = 13
So a string bag contains either 12 apples or 13 apples.