# Winona needs to average 5.8 points from 14 judges to win the competition. The mean scores from 13 judges were 5.9. What is the lowest score she can get from the fourteenth judge and still win?

## 5.9(13/14)+x(1/14)=5.8 and solve for x

## To find the lowest score Winona can get from the fourteenth judge and still win the competition, we need to determine the total score she needs from the 14 judges.

Since Winona needs an average of 5.8 points from the 14 judges, the total score she needs would be the average multiplied by the number of judges:

Total score = Average score × Number of judges

Total score = 5.8 points × 14 judges = 81.2 points

Now, we know that the mean score from the first 13 judges was 5.9 points. To find the total score from those 13 judges, we can multiply the mean score by the number of judges:

Total score from first 13 judges = Mean score × Number of judges

Total score from first 13 judges = 5.9 points × 13 judges = 76.7 points

To find the minimum score Winona can get from the 14th judge and still win, we subtract the total score from the first 13 judges from the total score Winona needs:

Minimum score from the 14th judge = Total score - Total score from first 13 judges

Minimum score from the 14th judge = 81.2 points - 76.7 points

Minimum score from the 14th judge = 4.5 points

Therefore, the lowest score Winona can get from the fourteenth judge and still win the competition is 4.5 points.