To find the two consecutive even numbers whose sum is 146, follow these steps:
1. Understand the problem: We need to find two even numbers that are consecutive and add up to 146. Let's call the first even number [tex]\( n \)[/tex]. Since the numbers are consecutive even numbers, the next even number will be [tex]\( n + 2 \)[/tex].
2. Set up the equation: According to the problem, the sum of these two numbers is 146. Therefore, we can write the equation:
[tex]\[
n + (n + 2) = 146
\][/tex]
3. Simplify the equation: Combine like terms to simplify the equation:
[tex]\[
n + n + 2 = 146 \implies 2n + 2 = 146
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
- Subtract 2 from both sides to isolate the term with [tex]\( n \)[/tex]:
[tex]\[
2n + 2 - 2 = 146 - 2 \implies 2n = 144
\][/tex]
- Divide both sides by 2 to solve for [tex]\( n \)[/tex]:
[tex]\[
\frac{2n}{2} = \frac{144}{2} \implies n = 72
\][/tex]
5. Find the consecutive even number: Now that we have [tex]\( n = 72 \)[/tex], the next consecutive even number is:
[tex]\[
n + 2 = 72 + 2 = 74
\][/tex]
Therefore, the two consecutive even numbers whose sum is 146 are [tex]\( 72 \)[/tex] and [tex]\( 74 \)[/tex].
