Problema Solution
Tom, Tim and Kyle are anglers. Their fishing boat has a 440 pound weight limit. The average weight of the two lighter anglers is 115 pounds. The average weight of the two heavier anglers is 200 pounds. If the median weight of the anglers is 160 pounds, will they be over or under the boat's weight limit? How much do Tom, Tim, and Kyle weigh?
Answer provided by our tutors
Let
x = Tom's weight, x>0
y = Tim's weight, y>0
z = Kyle's weight, z>0
We will assume that x <= y <= z.
The average weight of the two lighter anglers is 115 pounds:
(1/2)(x + y) = 115
The average weight of the two heavier anglers is 200 pounds:
(1/2)(y + z) = 200
The median weight of the anglers is 160 pounds.
The median value is y thus y = 160 lbs.
(1/2)(x + 2y + z) = 115 + 200
x + y + z + y = 2*315
x + y + z = 630 - y
x + y + z = 630 - 160
x + y + z = 470 lbs > 430
The will be over the boat's weight limit.
By solving
(1/2)(x + 160) = 115
(1/2)(160 + z) = 200
........
........
x = 70 lbs
y = 160 lbs
z = 240 lbs
Tom weights 70 lbs.
Tim weights 160 lbs.
Kyle weights 240 lbs.