If |a-b| = 5 and |a-c| = 3, which of the following could be the value of |b-c|?

Question

I. 2

II. 4

III. 8

 

which combination and why?

Answer 1

Here's the way I'd figure it out...

 

|a-b| = 5 means that a - b = 5  or  a - b = -5

 

Multiply both of those equations through by -1 and you get

 

b - a = -5 or b - a = 5

 

Now |a-c| = 3 means that a - c = 3  or a - c = -3

 

So add each of the equations for b-a to each of the equations for a-c.

 

That's going to give you 4 equations for b-c.  The different values of b-c are going to be 8, -8, 2, and -2.

 

So |b-c| is either 8 or 2.