Question

What are $3$consecutive numbers whose sum is $54$?

Answer 1

Hint: We will use the concept of consecutive numbers. There is a difference of 1 between two consecutive numbers. For example, $1,2,3{\text{ and 10,11,12}}$ are the consecutive numbers.

Complete step-by-step answer:
Let us assume the first integer be “x” ….. (A)
The second consecutive integer be ….. (B)
And the third consecutive integer be ….. (C)
Given that the sum of the three consecutive odd integers is $54$
So, the equation becomes-
$x + (x + 1) + (x + 2) = 54$
Simplify the above equations by pairing the like terms together.
$ \Rightarrow \underline {x + x + x} + \underline {1 + 2} = 54$
Add the like terms-
$ \Rightarrow 3x + 3 = 54$
Move all like terms on one side of the equation. When you move any term from one side of the equation to the opposite side, then the sign of the terms also changes. Positive terms become negative and negative terms become positive.
$ \Rightarrow 3x = 54 - 3$
Simplify the above equation finding the difference on the right hand side of the equation-
$ \Rightarrow 3x = 51$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow x = \dfrac{{51}}{3}$
Find factors for the term on the numerator.
$ \Rightarrow x = \dfrac{{3 \times 17}}{3}$
Common factors from the numerator and the denominator cancel each other.
$ \Rightarrow x = 17$
By using equations (A), (B) and (C)
Therefore, the three consecutive numbers are $17,18,19$
So, the correct answer is “$17,18,19$”.

Note: In simple words, consecutive numbers are the numbers which follows each other continuously in order from the smallest to the largest. In these types of problems, we use the concept of consecutive numbers and adding 1 to number we can get next number, subtracting 1 from the number we can ger preceding number. As it is not mentioning the type of number so we will consider it as the natural number. If it will be Even or Odd number, we need to take difference of 2 between two consecutives Even or Odd numbers depending on the mentioned condition.