Madeline has eight dogs. The mean weight of the lightest six is 40 pounds. The mean weight of the heaviest six is 55 pounds. What is the greatest possible range of weights of her dogs?
Here is my attempt at this:
The lightest 6 dogs average =240/6 =40 lbs
The heaviest 6 dogs average=330/6=55 lbs
The average weight of the 8 dogs =47.50 lbs[40+55]/2
H = Heaviest
8 * 47.50 - 2H = 240 lbs, solve for H
H =70 lbs * 2 =140 lbs - combined weight of 2 heaviest dogs.
The heaviest dog must have a maximum weight of: 140 - 55 = 85 lbs
L = Lightest
8 * 47.50 - 2L =330 lbs, solve for L
L=25 lbs * 2 = 50 lbs - combined weight of 2 lightest dogs.
The lightest dog must have a minimum weight of: 50 -40 =10 lbs.
Therefore, the 8 dogs' weights will range from 10 lbs - being the minimum weight - to 85 lbs - being the maximum weight.
