The sum of three consecutive multiples of 3 is 99. These multiples are

Question

Accepted Answer

The question asks for three consecutive multiples of 3 whose sum is 99.

Let's analyze the options:

**1. Justification for Option 3 being correct:**
*   **Option 3: 30, 33, 36**
    *   **Are they multiples of 3?** Yes, 30 = 3 × 10, 33 = 3 × 11, and 36 = 3 × 12.
    *   **Are they consecutive multiples of 3?** Yes, the difference between consecutive numbers is 3 (33 - 30 = 3, 36 - 33 = 3). This means they are indeed consecutive multiples of 3.
    *   **Is their sum 99?** 30 + 33 + 36 = 99.
    *   Since all conditions (multiples of 3, consecutive, and sum is 99) are met, Option 3 is the correct answer.

*Alternatively, we can solve this algebraically:*
    Let the three consecutive multiples of 3 be $x$, $x+3$, and $x+6$.
    Their sum is $x + (x+3) + (x+6) = 99$.
    $3x + 9 = 99$.
    $3x = 99 - 9$.
    $3x = 90$.
    $x = 30$.
    So the three multiples are 30, 30+3=33, and 30+6=36. This matches Option 3.

**2. Explanation for why other options are incorrect:**

*   **Option 1: 24, 33, 42**
    *   **Are they multiples of 3?** Yes (24 = 3 × 8, 33 = 3 × 11, 42 = 3 × 14).
    *   **Are they consecutive multiples of 3?** No. The difference between 33 and 24 is 9, and the difference between 42 and 33 is 9. For them to be consecutive multiples of 3, the difference should be 3.
    *   **Is their sum 99?** 24 + 33 + 42 = 99. While the sum is correct, the numbers are not *consecutive* multiples of 3. Therefore, this option is incorrect.

*   **Option 2: 32, 33, 34**
    *   **Are they multiples of 3?** No. 32 is not a multiple of 3 (32 ÷ 3 is not an integer), and 34 is not a multiple of 3 (34 ÷ 3 is not an integer). Only 33 is a multiple of 3.
    *   **Are they consecutive?** Yes, they are consecutive integers, but not consecutive *multiples of 3*.
    *   **Is their sum 99?** 32 + 33 + 34 = 99. While the sum is correct, the numbers themselves are not all multiples of 3. Therefore, this option is incorrect.

*   **Option 4: None of these**
    *   Since Option 3 correctly identifies the three consecutive multiples of 3 whose sum is 99, this option is incorrect.

The final answer is $\boxed{	ext{3}}$