SOLUTION: 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.
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Question 257442: 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 by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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.
.
From:"The average of a and b is x." we get:
(a+b)/2 = x
From:"The average of b and x equals the average of a and (b + 1)" we get:
(b+x)/2 = (a+b+1)/2
.
(b+(a+b)/2)/2 = (a+b+1)/2
(b+(a+b))/2 = a+b+1
(b+a+b)/2 = a+b+1
(2b+a)/2 = a+b+1
2b+a = 2a+2b+2
a = 2a+2
-2 = a
.
(a+b)/2 = x
(-2+b)/2 = x
-2+b = 2x
b = 2x+2
.
Therefore,
a-b = -2 - (2x+2)
a-b = -2 - 2x-2
a-b = -4-2x
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