Question

Find three consecutive even integers whose sum is$234$.

Short answer

The sum of three consecutive even integers $76,78,\&80$is$234$.

Step-by-step solution

Step 1. Given information    

The sum of three consecutive even integers is$234$.

Step 2. Name the integers

Consider first even integer is n.

second consecutive even integer is $n+2$.

Third consecutive even integer is $n+4$.

Step 3. Solution

The sum of three consecutive even integers is $234$

$$\begin{gathered} n+(n+2)+(n+4)=234 \\ 3n+6=234 \\ 3n=228 \\ n=76 \end{gathered}$$

So the first integer is$n=76$

Step 4. Value of consecutive even integers 

Second consecutive even integer

$$\begin{gathered} n+2=76+2 \\ =78 \end{gathered}$$

So Second consecutive even integer is$78$

Third consecutive even integer

$$\begin{gathered} n+4=76+4 \\ =80 \end{gathered}$$

the third consecutive integer is$80$

So three consecutive integers arerole="math" localid="1647204442965" $76,78,\&80$

Step 5. Verification 

Sum of $76,78,\&80$is$234$

$$\begin{gathered} 76+78+80\stackrel{?}{=}234 \\ 234=234 \end{gathered}$$

The left-hand side is equal to the right-hand side, so our answer is correct

Three consecutive even integers are$76,78,\&80$.