Anne has boxes in three sizes: large, medium, and small.

She puts 11 large boxes on a table. She leaves some of these boxes empty, and in each of the other boxes she puts 8 medium boxes. She leaves some of these medium boxes empty, and in each of the other medium boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty.

How many boxes has Anne used in total?

You start with 11 empty boxes.  Boxes are added in groups of 8, all empty to begin with, but filling a previously empty box, for a net gain of 7 in the count of empty boxes.

As there are 102-11=91 more empty boxes now than at the beginning, the process of adding 8 boxes was done 91/7 = 13 times. So there are 11 + 8*13 = 115 boxes now present.

Posted by Charlie on 2009-01-26 14:40:35