There are 3 natural numbers. If the average of any 2 numbers is added with the third number 34, 30 and 28 will be obtained. Find the numbers.
Let the numbers be a, b and c Now (a+b)/2 + c = 34 …………………. (i) (a+c)/2 + b = 30 ………………….(ii) (b+c)/2 + a = 28 ………………….(iii) By solving the equations, we get a + b + 2c = 68 a + c + 2b = 60 b + c + 2a = 56 by adding above equations we get, 4a + 4b + 4c = 184 a + b + c = 46 from equation (i), (a+b)/2 + c = 34 a + b + c + c =34 × 2 46 + c = 68 c = 22 similarly from equation (ii) and (iii) b = 14 and a = 10
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