At an archery competition, 6 men scored an average of 54 points. The winners score was 4 points more than that of the runner up. The average score of the rest was 47 points. How many points did the winner score?
Let's denote the score of the winner as W and the score of the runner up as R.
From the information given, we can set up the following equations:
1) (6 * 54) = 324 (total points scored by the 6 men)
2) W = R + 4
3) (6 * 47) = 282 (total points scored by the rest of the men)
We can substitute the values from equations 1 and 2 into equation 3 to solve for W:
6W = 324 + 282
6W = 606
W = 101
Therefore, the winner scored 101 points.