Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?
A.82
B. 118
C. 120
D. 134
E. 152
視頻解析
文字解析
_,_,_,84,_,_
中位數(shù)84已經(jīng)固定,后三位不可能比84小,所以要保證最后一位足夠大的策略就是后兩位也為84,且前三位都取最小數(shù)。
設(shè)最小一位為x,則數(shù)列變?yōu)閤,x,x,84,84,84,4x+14。再根據(jù)7個(gè)數(shù)總和為476,算出x=30,則最大數(shù)4x+14為134。
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