Math Word Problem
posted by Linda .
Counting Chicken Wings
At Annie's HomeCooked Chicken Wings Restaurant, chicken wings are served by the bucket. The Biggest Bucket O'Wings is really big! Figure out how many wings are in the bucket.
If the wings are removed two at a time, one wing will be left. If they're removed three at a time, two wings will remain. If they're removed four at a time, then three will remain; if they're removed five at a time, then four will remain; and if six at a time are taken from the bucket, then five wings will remain. If they're taken out seven at a time, no wings will be left over.
What's the smallest possible number of wings that could be in the bucket? EXPLAIN YOUR ANSWER THOROUGHLY!!!

The number must be evenly divisible by 7. It must also be odd, since taking two at a time leaves 1. It must be two more than a multiple of 3, etc..
What can work?
Not 7 (3 at a time leaves 1)
Not 21 (3 at a time leaves none)
35? No. Five at a time leaves none.
49? No. Three at a times leaves 1
63? No. Three a time leaves none
77? No. Four at a time leaves 1
91? No. Three at a time leaves 1
119? Try it. 
the coach is building shelves to store and organize the team's collection of 175 game videos. how many shelves will be needed if one shelf holds 28 videos?