How many apples are there in a string bag if there are more than eleven apples in a string bag? Find all possible solutions.
A shopkeeper gets apples from two suppliers: one delivers apples in boxes, the other in bags. There are always the same number of apples in each of the boxes. This is also true when talking about bags though a box and a bag may contain a diffamount number of apples. Every day when the shopkeeper gets the apples from the suppliers, he repacks them into string bags. One day, theshopkeeper received nine boxes and three bags. When he repacks the apples into eleven string bags, he had less than ninety-seven apples left. Another day, he got six boxes and two bags. After he repacks them into eight string bags, he had at least fifty-six apples left. How many apples are there in a string bag if there are more than eleven apples in a string bag? Find all possible solutions.
Let the number of apples in the boxes that the shopkeeper receives be X and the number of apples in the bags be Y. Let the number of apples put in each string bag be S.
On the day he received nine boxes and three bags he repacked them in 11 string bags and had at least 97 apples left.
=> 11*S + 97 = 9*X + 3*Y
The following day when he got 6 boxes and 2 bags and repacked them in 8 string bags and there were at least 56 apples left.
=> 8*S + 56 = 6*X + 2*Y
The number of apples received on the second day is (2/3) the number received on the first day. If the number of apples received is (2/3) the number of apples that can be packed in the string bags is also (2/3).
=> (11*S + 97)*(2/3) = 8*S + 56
=> 22*S + 194 = 24*S + 168
=> 2S = 26
=> S = 13
As it is known that there are more than 11 apples in a string bag, the number of apples in a bag can be either 12 or 13.
There are either 12 or 13 apples in each string bag.