Question

The sum of three consecutive integers is 78. Find the integers.

Short answer

The integers are $25,26,27$.

Step-by-step solution

Step 1. Given information 

We have been given that the sum of three consecutive integers is 78.

We have to find the integers.

Step 2. Form the equations

Let the one integer be $x$,

From the statement: The sum of three consecutive integers is 78 .

We get :

$x+(x+1)+(x+2)=78$

Step 3. Solve for the equations

Solve the equation for x,

$$\begin{gathered} x+(x+1)+(x+2)=78 \\ 3x+3=78 \\ 3x=75 \\ x=\frac{75}{3} \\ x=25 \end{gathered}$$

The second integer will be,

$$\begin{gathered} x+1 \\ =25+1 \\ =26 \end{gathered}$$

Similarly, the third integer will be :$$\begin{gathered} 26+1 \\ =27 \end{gathered}$$