Question

The sum of four consecutive odd integers is $216$. What are the four integers?

Answer 1

Step 1: Natural numbers and Odd numbers

Natural numbers

Natural numbers are a part of the number system which includes all the positive integers from $1$ till infinity and are also used for counting purpose.

Odd numbers

Odd numbers are the numbers that cannot be divided by $2$ evenly.

Step 2: Let $x,x+2,x+4$ and $x+6$ be the four consecutive odd integers.

According to the given,

$\begin{array}{rcl}x+x+2+x+4+x+6& =& 216\\ 4x+12& =& 216\\ 4x& =& 216–12\\ 4x& =& 204\\ x& =& \frac{204}{4}\\ x& =& 51\end{array}$

Thus, the four consecutive integers are

$\begin{array}{rcl}x& =& 51\\ x+2& =& 53\\ x+4& =& 55\\ x+6& =& 57\end{array}$

Hence, the four numbers are $51,53,55,57$.