Four packages have an average weight of 11.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 10 pounds?  Choices: A) 11 B) 11.5 C) 13 D) 15 E) 16
Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 10 pounds. Therefore (b + c) / 2 = 10.   b + c = 20   The average is 11.5 pounds. Therefore (a + b + c + d) / 4 = 11.5.   a + (b + c) + d = 46   a + 20 + d = 46   a + d = 26   The weight a must be no greater than 10, since 10 is the median. Therefore the minimum possible weight of the heaviest package is 26 – 10 = 16 pounds (all the other packages would weigh 10 pounds in this case).   Answer: 16
<result>E</result>
Four packages have an average weight of 11.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 10 pounds?