Three consecutive integers add up to 51. What are these integers?

Hint: We will first consider the given statement as we need to find the three consecutive integers then we will let the same as \[x,x + 1,x + 2\]. Since the sum of three consecutive integers is given as 51 so, we will form the equation and find the value of \[x\]. As we get the one number \[x\], we can easily calculate the other two numbers by substituting the value of \[x\] and hence get the desired result.

Complete step-by-step answer:
We will first consider the given statement that the sum of three consecutive integers are 51.
The objective is to find the three consecutive integers,
We will first let the three consecutive integers as \[x,x + 1,x + 2\].
Now, as given in the question that the sum of three integers are 51 so, we will form the equation,
Thus, we get,
\[ \Rightarrow x + x + 1 + x + 2 = 51\]
Now, we will add the like terms and simplify the equation for \[x\],
\[
   \Rightarrow 3x + 3 = 51 \\
   \Rightarrow 3x = 48 \\
 \]
Next, we will divide the obtained equation by 3.
Thus, we get,
\[
   \Rightarrow \dfrac{{3x}}{3} = \dfrac{{48}}{3} \\
   \Rightarrow x = 16 \\
 \]
Hence, we get the one number as 16.
Now, we will find the other two numbers by substituting the value of \[x\].
Thus, we have,
\[
  x + 1 = 16 + 1 \\
   = 17 \\
 \] and \[
  x + 2 = 16 + 2 \\
   = 18 \\
 \]
Hence, we can conclude that the consecutive numbers are 16, 17 and 18.

Note: Consecutive integers are those which follow each other. So, that’s why we have the numbers which follow each other. Form the equation properly using the given statement to evaluate the value of \[x\]. Substitute the value properly in the expression to find the other integers. We can verify the result by checking if the numbers follow each other or not.