Question

The sum of two consecutive even numbers is $74$. Find the numbers.

Answer 1

Hint: First we assume the two consecutive even numbers are $x$ and $x+2$. Then as given in the question the sum of these two numbers is $74$, so we add the assumed numbers and equate the sum to $74$. Then solve the equation formed to obtain the desired answer.

Complete step-by-step answer:
We have been given that the sum of two consecutive even numbers is $74$.
We have to find the numbers.
Now, let us assume the two consecutive even numbers be $x$ and $x+2$.
As we know that the even numbers are divided by $2$.
Now, according to question, the sum of these two numbers is $74$, then we have
$x+\left( x+2 \right)=74$
Now, simplify the above equation we get
$\begin{align}
  & x+x+2=74 \\
 & 2x=74-2 \\
 & 2x=72 \\
 & x=\dfrac{72}{2} \\
 & x=36 \\
\end{align}$
So, the first even number is $36$.
Now, the second even number will be $x+2=36+2=38$
So, two consecutive even numbers are $36$ and $38$.

Note: Even numbers are the numbers exactly divisible by $2$, it means if even numbers are divided by $2$ gives the remainder zero. Some even numbers are $2,4,6,8........$ . The point to note in this question is that we assume the second consecutive number to be $x+2$ instead of $x+1$. If we add $1$ to any even number it will become odd. For example let an even number $12$, now if we add $1$ $\left( 12+1 \right)$ gives the number $13$, which is an odd number. So, to make a number consecutive even number we have to add $2$.