Question

# Find three consecutive odd numbers whose sum is 219.

Hint: In this question assume any variable x, to be an odd number and use the concept that if x is an odd number then the next consecutive odd number will differ from this number by 2, and the same carries on to find the next consecutive of the obtained number.

Let the first odd number be x.
Now if we add 1 in the odd number it becomes even so we have to add 2 so that it again becomes an odd number.
So the second consecutive odd number is (x + 2).
And the third consecutive odd number is [(x + 2) + 2] = x + 4.
Now it is given that the sum of three consecutive odd numbers is 219.
$\Rightarrow x + x + 2 + x + 4 = 219$
Now simplify the above equation we have,
$\Rightarrow 3x = 219 - 6 = 213$
Now divide by 3 throughout we have,
$\Rightarrow x = 71$
So the second odd number is (71 + 2) = 73.
And the third consecutive odd number is (73 + 2) = 75
So the three consecutive odd numbers are 71, 73 and 75 whose sum is 219.
So this is the required answer.

Note: Whenever we face such types of problems the key concept is to form the three consecutive odd numbers whose sum is to be calculated. As these numbers are formed, the constraints of the question helps forming equations and evaluation of these equations helps getting the answer to problems of this kind.