At the local recycling plant they are very good about using up every bit of scrap. From every seven bottles they can make one new one. How many new bottles can they make after recycling 221 bottles?

-Ray.

I believe the answer is 36. This is disturbing, because if the answer is not 42, you are asking the wrong question.

221 = 31 x 7 + 4 : make 31 new bottles, with 4 left over

31 + 4 = 5 x 7 : use those 31 and the leftover 4 to make 5 new bottles

you are now down to 5 bottles, so you can't make any more

this is assuming they get the bottles they make back after they are used

How many bottles can you make from n bottles?

They can make 36 recycled bottles. The make 31 the first time, with 4 left over. The 31 can be turned into 4, with 3 left over, and those 7 can be made into 1 more, for a total of 36 bottles.

-Ray.