In a candy shop, the shopkeeper allows the exchange of 3 sweet rappers for 1 new sweet. John has 81 sweets at first. What is the largest possible number of sweets that john could have eaten?
(with solution pls... tnx...)
81 wrappers gets 27 more
27 wrappers gets 9 more
9 wrappers gets 3 more
3 wrappers gets 1 more
81+27+9+3+1 = 121
To find the largest possible number of sweets that John could have eaten, we need to determine the number of sweets he would have left after exchanging sweet wrappers.
Since John starts with 81 sweets, we know that he can exchange wrappers for new sweets. According to the information given, 3 sweet wrappers can be exchanged for 1 new sweet.
To understand the process, we can examine it step by step:
1. Initially, John has 81 sweets.
2. He can eat all the sweets, which means he would have 0 sweets left and 81 wrappers.
3. He can then exchange all the wrappers for new sweets. Since he has 81 wrappers, he can exchange them for 27 new sweets (81 wrappers / 3 wrappers = 27 new sweets).
4. John could eat these 27 new sweets, leaving him with 0 sweets again and accumulating 27 more wrappers.
5. He can exchange these 27 wrappers for 9 more sweets (27 wrappers / 3 wrappers = 9 new sweets).
6. John could eat these 9 new sweets, leaving him with 0 sweets and an additional 9 wrappers.
7. Once again, he can exchange these 9 wrappers for 3 new sweets (9 wrappers / 3 wrappers = 3 new sweets).
8. Finally, John could eat these last 3 sweets, leaving him with 0 sweets and 3 more wrappers.
Since he cannot exchange 3 wrappers for another sweet, this is the point where John cannot eat any more sweets. Therefore, the largest possible number of sweets John could have eaten is 81 + 27 + 9 + 3 = 120 sweets.
So, the answer is 120.