Question
There are three numbers. If the average of any two of
them is added to the third number, the sums obtained are 177, 163 and 138. Whatis the average of the largest and the smallest of the given numbers?Solution
Let the three numbers be x, y, z. X+y / 2 + z = 177 x + y + 2z = 354 …(1) Y + z / 2 + X = 163 2x + y + z = 326 …(2) x + z / 2 + y = 138 x + 2y + z = 276 …(3) Adding eq(1),(2),(3) and dividing it by 4, we get x + y + z = 239 ,,,(4) sub (1) - (4), z = 115 sub (2) - (4), x = 87 sub (3) - (4), y = 37 The average of largest and smallest = 115+37/2 = 76
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