Expert: Scott A Wilson - 1/21/2010

Question
The average of a and b is x. The average of b and x equals the average of a and (b + 1). Find a - b.


Answer
It all comes down to determining the equations.
The average of a and b is x means that (a+b)/2 = x.

The average of b and x equals the average of a and (b + 1) means
(b+x)/2 = (a+b+1)/2.  Solving this for x meanas first lets multiply by 2.
This gives b+x = a+b+1.  Subtracting b gives x = a + 1.

Taking x = a + 1 and putting it into (a+b)/2 = x gives (a+b)/2 = a + 1.
This means that a+b = 2a+2.  Subtract a from both sides to get b = a + 2.

Since we are looking for a - b, subtrct b and subtract 2 from both sides.
It can be seen that subtracting b+2 from both sides gives -2 = a - b.

So even though we don't know what a and b are, a - b = -2.