You need exactly 47 bottles of water. you don’t want to buy more than you need, but you want the least expensive way. list the best way to buy exactly 47 bottles of water. single bottle: $1.25 6-pack: $7.20 12-pack: $13.80 case (20): $26.40

If you bought single bottles it would be 1.25*47= $58.75 
6-pack: If you bought exactly 8 6-packs you would get 48 which is one more than what you want AND it would cost you $57.60 which is cheaper than buying single bottles, but you are getting one more than what you need.
12-pack: 4 12-packs would be 48 bottles of water which is, once again, 1 more than what you need. It also costs 55.20 (it just keeps getting cheaper!)
Now for a case of 20: We don't even need to calculate this or anything because it would be way more than what you need (60 bottles because 40 wouldn't work) and it would be the most expensive. 
So by what i've shown you the cheapest way is to ,if you can only choose one, get 4 12 packs. Unless you can mix it up a bit and buy 3 12 packs and 1 6 pack and 5 singles. (54.85 in total)
Hoping this wasn't too confusing and I helped a bit

2 (20 packs=$52.80
1 (6 pack=$7.20
1 (1 bottle=$1.25
altogether you spend $61.25 and have 47 bottles
hope i helped!!!