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The sum of three consecutive even integers is 66. Which equation represents this scenario?

A. [tex]x = 66[/tex]

B. [tex]x + (x + 1) + (x + 2) = 66[/tex]

C. [tex]x + x + x = 66[/tex]

D. [tex]x + (x + 2) + (x + 4) = 66[/tex]

Answer :

To solve the problem of finding three consecutive even integers that add up to 66, let's break it down step by step.

1. Define Variables:
Let's define the first even integer as [tex]\( x \)[/tex].

2. Identify Consecutive Even Integers:
- The next consecutive even integer would be [tex]\( x + 2 \)[/tex].
- The one after that would be [tex]\( x + 4 \)[/tex].

3. Set Up the Equation:
Since the problem states that the sum of these three consecutive even integers is 66, we can write the equation:
[tex]\[
x + (x + 2) + (x + 4) = 66
\][/tex]

4. Simplify the Equation:
Combine the terms on the left side:
[tex]\[
3x + 6 = 66
\][/tex]

5. Solve for [tex]\( x \)[/tex]:
- Subtract 6 from both sides:
[tex]\[
3x = 60
\][/tex]
- Divide by 3:
[tex]\[
x = 20
\][/tex]

6. Find the Consecutive Integers:
Now that we know [tex]\( x = 20 \)[/tex]:
- The first integer is 20.
- The second integer is [tex]\( 20 + 2 = 22 \)[/tex].
- The third integer is [tex]\( 20 + 4 = 24 \)[/tex].

7. Conclusion:
The three consecutive even integers that add up to 66 are 20, 22, and 24.

The equation that represents this scenario is [tex]\( x + (x + 2) + (x + 4) = 66 \)[/tex], as outlined in the solution.

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