Question

How do you find two consecutive odd integers whose sum is \[36\]?

Answer 1

Hint: Here, we will find the two consecutive integers. We will assume the consecutive Integers to be some variables. Then by the given condition, we will frame a linear equation. Then by solving the linear equation, we will find the value of the variables, and thus, the two consecutive odd integers are the required answer.

Complete step by step solution:
Let \[x\] be the first odd integer and \[x + 2\] be the second odd integer.
So, \[x,x + 2\] are the two consecutive odd integers.
We are given that the sum of two consecutive odd integers is \[36\].
\[ x + x + 2 = 36\]
By adding the terms, we get
\[ \Rightarrow 2x + 2 = 36\]
By rewriting the terms, we get
\[ \Rightarrow 2x = 36 - 2\]
By subtracting the terms, we get
\[ \Rightarrow 2x = 34\]
By rewriting the terms, we get
\[ \Rightarrow x = \dfrac{{34}}{2}\]
By dividing by 2, we get
\[ \Rightarrow x = 17\]
The second odd integer \[x + 2\] is \[17 + 2 = 19\].

Therefore, the two consecutive odd integers whose sum is \[36\] are \[17,19\].

Note:
We know that a linear equation is defined as an equation with the highest degree as one. Linear equations are a combination of constants and variables. Constants are the numbers whereas variables are represented in letters. We should also know that every linear equation in one variable has a one and unique solution. We can solve the linear equation easily. First, we have to put the variable on the left-hand side and the numerical values on the right-hand side and then Change the operators while changing sides of the terms we can solve for the variable. We should be careful that if the given is in the form of consecutive odd integers, then it has to be added by the consecutive even numbers and if the given is in the form of consecutive even integers, then it has to be added by the consecutive odd numbers.