You're dealing with an unknown quantity here, and algebra is used to deal with unknown quantities. It seems rather superfluous at best not to use algebra, but I'll try to stay away from the dreaded variable (x).

1/5 is the rule

Sam's shorts were 3/7 of the rule. Thus Sam's shorts, being 6 inches, were 3/7 times 1/5 or 3/35 off the rule.

Now, ask yourself, 3/35 of something must equal 6. Guess what it is.

Now, some people might think the word "something" could be misconstrued as a variable. If that be the case, I guess I used algebra to solve it.