Five empty bottles can be exchanged for one bottle of soda. A class of students drank 161 bottles of soda, some of which were exchanged with the remaining empty bottles, so they should at least buy soda

Five empty bottles can be exchanged for one bottle of soda. A class of students drank 161 bottles of soda, some of which were exchanged with the remaining empty bottles, so they should at least buy soda

When you drink six bottles, you actually buy five bottles. When you finish the sixth bottle, you only have one bottle on hand. You need to buy four more bottles to replace one bottle. So when you drink 11 bottles, you buy nine bottles, and so on. If you drink 16 bottles and buy 13 bottles ·························, then the number of bottles you drink is 6N - (n-1) = 5N + 1, and the number you buy is 5N - (n-1) = 4N + 1
So 5N + 1 = 161 gives n = 32, which is substituted into 4N + 1 = 129 bottles

Five empty bottles can be exchanged for one bottle of soda. A class drank 161 bottles of soda, so how many bottles of soda did their class buy at least

I bought x bottles,
x+(x/5)+x/25+x/125=161
x=129
So at least 129 bottles