Question

The sum of three consecutive odd numbers is 51. Find the numbers.

Answer 1

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

Complete step-by-step answer:

Given data,
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 + 4 = 3x + 6.
According to the given, 3x + 6 = 51.
⟹3x = 51 – 6
⟹x =$\dfrac{{45}}{3} = 15$.
Hence, the numbers are 15, 17 and 19.

Note: In order to solve this type of questions the key is to consider a variable to be odd 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 gives an odd number itself.