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?

Answer 1

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.