THE ABBOT'S PUZZLE

The first English puzzlist whose name has come down to us was a Yorkshireman—no other than Alcuin, Abbot of Canterbury (A.D. `735-804`). Here is a little puzzle from his works, which is at least interesting on account of its antiquity. "If `100` bushels of corn were distributed among `100` people in such a manner that each man received three bushels, each woman two, and each child half a bushel, how many men, women, and children were there?"

Now, there are six different correct answers, if we exclude a case where there would be no women. But let us say that there were just five times as many women as men, then what is the correct solution?