Sure! Let's solve the problem step by step.
We are given that the sum of an even number and the succeeding fourth even number is 48. We need to find the original even number.
1. Define the even number:
Let the even number be [tex]\( x \)[/tex].
2. Determine the fourth succeeding even number:
Even numbers increase by 2. The first succeeding even number is [tex]\( x + 2 \)[/tex], the second is [tex]\( x + 4 \)[/tex], the third is [tex]\( x + 6 \)[/tex], and the fourth succeeding even number is [tex]\( x + 8 \)[/tex].
3. Set up the equation:
The sum of the original even number and the succeeding fourth even number is given to be 48. Therefore, we can write the equation as:
[tex]\[
x + (x + 8) = 48
\][/tex]
4. Simplify the equation:
Combining like terms, we get:
[tex]\[
x + x + 8 = 48
\][/tex]
[tex]\[
2x + 8 = 48
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
Subtract 8 from both sides of the equation:
[tex]\[
2x = 40
\][/tex]
Divide both sides by 2:
[tex]\[
x = 20
\][/tex]
The even number is [tex]\( \boxed{20} \)[/tex].
So, the even number is 20.
