Question

find three consecutive intergers whose sum is 276

Answer 1

If we need to find three consecutive integers, we have that they can be written as follows:

$x,x+1,x+2$

Since the sum of all of them is equal to 276, we can write the following equation:

$x+(x+1)+(x+2)=276$

Now, adding like terms, we have:

$\begin{gathered} (x+x+x)+(1+2)=276 \\ 3x+3=276 \\ \end{gathered}$

Now, we can subtract 3 from both sides of the equation, and then divide by 3 as follows:

$\begin{gathered} 3x+3-3=276-3 \\ 3x=273 \\ \frac{3x}{3}=\frac{273}{3} \\ x=91 \end{gathered}$

Then, we have that:

$\begin{gathered} x=91 \\ x+1=92 \\ x+2=93 \end{gathered}$

If we add these three consecutive integers, we will have:

$\begin{gathered} 91+92+93=276 \\ 276=276\Rightarrow This\text{ is True.} \end{gathered}$

In summary, the three consecutive integers whose sum is 276 are 91, 92, and 93.