Question

Mr. McCracken and his friends are going on a golf trip. He wants to make golf bags to take on the trip. He has 24 golf trees and 36 golf balls. Each golf bag must have the same number of golf trees and the same number of golf balls. What are the possible numbers of golf bags Mr. McCracken can make so that the golf trees and golf balls are shared equally? Describe each possibility.

Answer 1

There are in total Six cases possible - 1,2 ,3,4,6,12

Number of Golf Trees = 24

Number of Golf balls = 36

H.C.F [ Highest common factor] -

⇒ 24 = 2 * 2 * 2 * 3 * 1

⇒ 36 = 2 * 2 * 3 * 3 * 1

Case 1 ) Bag = 1 [ Total Golf trees = 24]

                           [ Golf trees = 36] [in each bag]

Case 2 ) Total Bags = 2

[Golf balls = 18]

[ Golf trees = 12] [in each bag]

Case 3 ) Total Bags = 3

Golf balls = 8

Golf trees = 10  [in each bag]

Case 4 ) Total Bags = 4

Golf balls = 9

Golf trees = 8 [in each bag]

Case 5 ) Total Bags = 6

Golf trees = 4

Golf balls = 6 [ in each bag ]

Case 6 ) Total Bags = 12

Golf balls = 3

Golf trees = 2 [ in each bag ]

Hence, There are in total Six cases possible - 1,2 ,3,4,6,12

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