SOLUTION: The mean of three numbers is 5/9. The difference between the largest and smallest number is 1/2, which happens to be one of the numbers. What is the smallest number? Express your a

Question 203413: The mean of three numbers is 5/9. The difference between the largest and smallest number is 1/2, which happens to be one of the numbers. What is the smallest number? Express your answer as a common fraction.
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let the three numbers be x, y, z in such a way that x < y < z.

Mean of the numbers:
i.e. ______ (1)

The difference between the largest and smallest number:
__________ (2)

One of the numbers is .
(A) If the largest number is then the smallest number would be and hence the sum of three numbers will be less than .
(B) If the smallest number is then the largest number would be and hence the middle number would be which is less than the smallest number .
Since options (A) and (B) results in contradiction with the given conditions, both of them are false. So the middle number is .
To solve for the numbers:
Adding both sides of equations (1) and (2) we have

But, y = middle number = .
So, i.e.

Thus,

Hence, the numbers are , and .
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