In a competition a total of 5 judges give out scores greater than 50. If the mean of his scores is 57, what is the highest amount of points he could have earned from one judge?
Please explain thoroughly. I know how to do mean, but I am not sure how to approach this problem.
If the mean of his scores is 57 and there are 5 judges, then his total score was 57*5=285. If each judge gives out a score greater than 50, then the lowest score a judge can give is 51. To find the highest amount of points he could have earned from one judge, we can assume that the other four give him the lowest possible score, 51. x+51*4=285 simplifies to x=81, so the highest score he could have earned from one judge is 81.