Question

Sum of three consecutive odd numbers is 153. What are the numbers?

Answer 1

Hint: To find the three consecutive odd numbers whose sum is equal to 153, let the first odd number be x. Hence, the second odd number should be x+2 and the third odd number should be x+4. Now, form the equation by adding these terms and equate them with 153. Solving the equation, you will get the value of x and all the three odd numbers.

Complete step-by-step answer:
In this question, we have to find three numbers that are consecutively odd and their sum is equal to 153.
That means, we have to find such 3 numbers that are odd and are also consecutive and their sum should equal to 153.
For finding those numbers, let us suppose that x is an odd number. So, the next number that is x+1 will be even and its next term that is x+2 will be odd. The next term that is x+3 will be again even and the next term that is x+4 will be odd. Hence, we have our all three terms.
$ \to $First odd number$ = x$
$ \to $Second odd number$ = x + 2$
$ \to $Third odd number$ = x + 4$
Now, we are given that their sum is equal to 153. Hence, we get an equation
$ \to x + \left( {x + 2} \right) + \left( {x + 4} \right) = 153$
Adding all x terms and taking constant terms to RHS, we get
$
   \to 3x = 153 - 2 - 4 \\
   \to 3x = 147 \\
 $
Now, dividing the equation on both sides with 3, we get
$
   \to \dfrac{{3x}}{3} = \dfrac{{147}}{3} \\
   \to x = 49 \\
 $
Hence, we got the value of x as 49. Therefore, the three numbers will be
$ \to $First odd number$ = x = 49$
$ \to $Second odd number$ = x + 2 = 49 + 2 = 51$
$ \to $Third odd number$ = x + 4 = 49 + 4 = 53$
Hence, the three consecutive odd numbers whose sum is equal to 153 are 49, 51 and 53.

Note: Note that the sum of three odd numbers is always equal to an odd number only. It anno be equal to an even number. Similarly, the sum of three even numbers is always equal to an even number only and it cannot be equal to odd number.