a) Suppose that \[|a - b| + |b - c| + |c - a| = 20.\] What is the maximum possible value of $|a - b|$?
b) Suppose that \[|a - b| + |b - c| + |c - d| + \dots + |m-n| + |n-o| + \cdots+ |x - y| + |y - z| + |z - a| = 20.\] What is the maximum possible value of $|a - n|$?
+128448 Here's the first one
Let a > c > b
And since a > b, then l a - b l = a - b
And since c > b, the l b - c l = c - b
And since a > c, then l c - a l = a - c
Then we have that
(a - b) + ( c - b) + ( a - c) = 20 simplify
2a - 2b = 20 divide through by 2
a - b = 10
And this is the max value for l a - b l
