Question

Find three consecutive integers whose sum is 366.

Answer 1

Hint: First, we let us suppose the first number is $x$. Then, the condition given in the question says that the numbers are three consecutive integers , so next numbers are $x+1$ and $x+2$.Then, by adding these three integers and equating it with 366, we get the final result.

Complete step-by-step answer:
In this question, we are supposed to find three consecutive integers whose sum is 366.
So, before proceeding for this , let us suppose the first number is $x$.
So, the condition given in the question says that the numbers are three consecutive integers.
So, by using the above condition, the next two integers of $x$ are $x+1$ and $x+2$.
Now, the question says that the addition of these three integers gives the sum of 366.
Then, by adding these three integers and equating it with 366 as:
$x+x+1+x+2=366$
Now, by using the above expression to find the value of $x$ as:
$\begin{align}
  & 3x+3=366 \\
 & \Rightarrow 3x=366-3 \\
 & \Rightarrow 3x=363 \\
 & \Rightarrow x=\dfrac{363}{3} \\
 & \Rightarrow x=121 \\
\end{align}$
So, it gives the value of the first number which we have supposed as $x$ is 121.
Now, the other two numbers are as follows:
$x+1=122$
$x+2=123$
So, the three consecutive numbers whose sum is 366 are 121, 122 and 123.
Before concluding it, we must cross verify by adding 121, 122 and 123 whether it gives the same result as desired or not.
So, addition of 121, 122 and 123 is:
$121+122+123=366$
Hence, the three consecutive numbers which sums to 366 are 121, 122 and 123.

Note: In these types of questions we must be careful with the conditions given in the questions as sometimes it is mentioned that the three even consecutive numbers sums 366 which leads to assumption that first number $x$. But the next numbers are $x+2$ and $x+4$ instead of $x+1$ and $x+2$. So, be careful while working with these types of conditions.