# Define three numbers,if the amount is given for every two of them

1
by violetta822
Hey is that the complete question ?
Yes

2015-04-24T01:15:11+05:30

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Three numbers are : X, Y, and Z.  We don't know these numbers yet.

Amount is given for every two of them.  Suppose the amounts are A, B and C.  These are known values.

X + Y = A      --- (1)
Y + Z = B      --- (2)
Z + X =  C      --- (3)

(1) - (2) + (3) gives,    2 X = (A-B+C)    =>    X = ( C + A - B) / 2
(1) + (2) - (3)  gives,      Y = (A + B - C) / 2
(2) + (3) - (1)  gives,      Z = (B + C - A) / 2

Hence, the value of the number is half of the difference between the sum of the amounts of the two pairs of which the number is part, and the amount of the pair in which the number is absent.

Thus,  X is present in the amounts A and C. Sum them.  Subtract B (in which X is not present).  Then divide the difference  by 2.

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