Question

How do you find three consecutive odd numbers whose sum is 51?

Answer 1

Hint:To find the odd numbers whose sum is 51, firstly we consider an odd number x, then write its next consecutive numbers, and finally add all of them and equate them to 51. Then we solve the equation for x.

Complete step-by-step solution-
According to the given data,
The Sum of 3 consecutive odd numbers is equal to 51.
Let the odd number be ‘x’. Then the next consecutive odd number becomes ‘x+2’ and the next term becomes x+2+2= ’x+4’.
Now the sum of these three odd consecutive terms = $x + x + 2 + x + 2 + 2 = 3x + 6$
Further according to the given question,
$3x + 6 = 51$
$ \Rightarrow 3x = 51 - 6$
$ \Rightarrow x = \dfrac{{45}}{3} = 15$
Therefore, the numbers are 15, 17 and 19.

Note- To solve these types of questions the main crux is to consider a variable to be an odd number and compute the sum of three consecutive odd numbers in terms of this variable. Then by solving for this variable we can determine the numbers. Any odd number added with 2 always gives an odd number itself.