Question

Write an equation and solve each problem. (Lesson2.3)

Find four consecutive integers with a sum of 106.

Short answer

Four consecutive numbers are 25, 26, 27, and 28.

Step-by-step solution

Step 1. Given Statement.

To find four consecutive integers with a sum of 106.

Step 2. Consecutive integers.

Consecutive integers can be written in the form as: $x,x+1,x+2,x+3,x+4$, and so on where x is any integer.

Step 3. Description of step.

In order to solve the problem, i.e. to find the four consecutive integers with sum of 106, take one number as x, then other three must be $x+1,x+2,x+3$.

Now, as given sum of these four consecutive integers is 106

Thus,

$\begin{array}{c}\left(x\right)+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)=106\\ x+x+1+x+2+x+3=106\\ 4x+6=106\\ 4x=106-6\\ \Rightarrow 4x=100\\ \Rightarrow x=\frac{100}{4}\\ \Rightarrow x=25\end{array}$

Thus, value of x is 25 and other numbers are

$\begin{array}{l}x+1=25+1=26\\ x+2=25+2=27\\ x+3=25+3=28\end{array}$

Therefore, required four consecutive numbers are 25, 26, 27, and 28.