Call Me Mr. Predictable
A cryptographer in deciphering an enemy message composed of an unbroken series of letters determines there are three words, each containing a different number of letters. From past experience he knows that the first word contains 3 letters less than the total number of letters in the other two words. The second word always contains 1/5 of 3 less than the total number of letters in the first and third words. The third word contains 1 letter less than the sum of the letters in the first two words. How many letters are there in each word?
Source: W.C. Eddy's Wartime Refresher in Fundamental Mathematics, 1945, p. 100