Average of Two Numbers

The average of a and b is x. The average of b and x equals the average of a and (b+1). Find the value of a-b.
Source: NCTM Mathematics Teacher 2008

SOLUTION
Average of a and b
\dfrac{a+b}{2}=x\qquad\qquad\qquad\: (1)
Average of b and x
\dfrac{b+x}{2}=\dfrac{a+(b+1)}{2}\qquad (2)
Simplify Eq. (2)
\dfrac{b+x}{2}=\dfrac{a+b}{2}+\dfrac{1}{2}
Substitute the value of \dfrac{a+b}{2} from Eq. (1)
\dfrac{b+x}{2}=x+\dfrac{1}{2}
Simplify
b+x=2x+1
x=b-1
Substitute the value of x into Eq. (1)
\dfrac{a+b}{2}=b-1
Simplify
a+b=2b-2
a-b=-2

Answer: -2

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About mvtrinh

Retired high school math teacher.
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