Question

How do you find two consecutive odd integers whose sum is $116$?

Answer 1

Step -1: Establish the equation:

Let the first odd integer be $x$.

Then, the next consecutive odd integer is $(x+2)$.

Given that the sum of the integers is $116$.

Then, we will write:

$x+(x+2)=116$

Step-2: Solve the equation:

Now we will simplify and solve the equation.

$x+x+2=116$

$\Rightarrow$$2x+2=116$

$\Rightarrow$ $2x=116-2$

$\Rightarrow$ $2x=114$

$\Rightarrow$ $x=\frac{114}{2}$

$\Rightarrow$ $x=57$

Step-3: Calculate the next integer:

Hence the next consecutive odd integer is,

$x+2=57+2$

$=59$

Hence, the required consecutive odd integers are $\mathbf{57}$ and $\mathbf{59}$.