若正数a,b,c满足不等式组11c/6＜a+b＜2c3a/2＜b+c＜5a/35b/2＜a+c＜11b/4则a、b、c的大小关系是A.a＜b＜cB.b＜c＜aC.c＜a＜bD.a＜c＜b要有详解

Question

若正数a,b,c满足不等式组
11c/6＜a+b＜2c
3a/2＜b+c＜5a/3
5b/2＜a+c＜11b/4
则a、b、c的大小关系是
A.a＜b＜c
B.b＜c＜a
C.c＜a＜b
D.a＜c＜b
要有详解

Answer 1

（11c/6＜a+b＜2c）*6=11c＜6a+6b＜12c ①
（3a/2＜b+c＜5a/3）*6=9a＜6b+6c＜10a ②
（5b/2＜a+c＜11b/4 ）*6=15b＜6a+6c＜33b/2 ③
①-②=11c-9a＜6a-6c＜12c-10a→17c+a＜16a ,16a＜18c→17c+a＜18c→a＜c
①-③=11c-15b＜6b-6c＜12c-33b/2→17c＜21b ,21b＜18c-3b/2→3b/2＜c→
→b+b/2＜c→b＜c
②-③=9a-15b＜6b-6a＜10a-33b/2→15a＜21b ,21b＜16a-3b/2→3b/2＜a→
→b+b/2＜a→b＜a
选B