Select the correct answerThe sum of three consecutive even numbers is 132. What is the smallest number?Options464442484

Step 1: Break Down the Problem

We need to find three consecutive even numbers whose sum is 132. We can denote the smallest of these even numbers as $x$. Therefore, the three consecutive even numbers can be expressed as:

• First number: $x$
• Second number: $x + 2$
• Third number: $x + 4$

Step 2: Relevant Concepts

To find the sum of these numbers, we will set up an equation based on the sum being 132: $x + (x + 2) + (x + 4) = 132$

Step 3: Analysis and Detail

Now, let's simplify the equation: $3x + 6 = 132$ Next, we will isolate $x$:

1. Subtract 6 from both sides: $3x = 132 - 6$ $3x = 126$
2. Now, divide both sides by 3: $x = \frac{126}{3}$ $x = 42$

Step 4: Verify and Summarize

To verify, let's write down the three numbers:

• First number: $42$
• Second number: $44$ (which is $42 + 2$)
• Third number: $46$ (which is $42 + 4$)

Now, check their sum: $42 + 44 + 46 = 132$ The calculation is correct.

Final Answer

The smallest number is $42$.