The best way figure out the number of smaller bags that can be made using 5000 wintergreen, 3000 spearmint, and 2000 peppermint is to find the number of smaller bags that could be created for each flavor of gum by itself. The smallest number of smaller bags out of all the flavors (if that makes sense!) is the maximum you can make.
1) How many bags of 100 wintergreen can you make with 5000 wintergreen?
5000/100 = 50 bags
2) How many bags of 30 spearmint can you make with 3000 spearmint?
3000/30 = 100 bags
3) How many bags of 20 peppermint can you make with 2000 peppermint?
2000/20 = 100 bags
Since you can only make 50 bags of 100 wintergreen with how much gum you're given in the large bag, that is the maximum number. You cannot make any more, even though you have plenty of spearmint and peppermint left over, because you don't have enough wintergreen.
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Answer: 50 smaller bags