The sum of three consecutive multiples of 3 is 72. What is the largest number?

Options

A. 21
B. 24
C. 27
D. 36

Answer

To solve the problem of finding the largest of three consecutive multiples of 3 that sum up to 72, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let the first multiple of 3 be represented as \(3x\). Since we are looking for three consecutive multiples of 3, the next two multiples can be represented as \(3(x+1)\) and \(3(x+2)\). Therefore, we can express the three consecutive multiples of 3 as:
- First multiple: \(3x\)
- Second multiple: \(3(x + 1) = 3x + 3\)
- Third multiple: \(3(x + 2) = 3x + 6\)

2. **Set Up the Equation**:
According to the problem, the sum of these three multiples is equal to 72. We can set up the equation:
\[ 3x + (3x + 3) + (3x + 6) = 72 \]

3. **Simplify the Equation**:
Combine like terms:
\[ 3x + 3x + 3 + 3x + 6 = 72 \]
This simplifies to:
\[ 9x + 9 = 72 \]

4. **Solve for \(x\)**:
To isolate \(x\), subtract 9 from both sides:
\[ 9x = 72 - 9 \]
\[ 9x = 63 \]
Now, divide both sides by 9:
\[ x = \frac{63}{9} = 7 \]

5. **Find the Consecutive Multiples**:
Now that we have \(x\), we can find the three consecutive multiples:
- First multiple: \(3x = 3 \times 7 = 21\)
- Second multiple: \(3(x + 1) = 3 \times 8 = 24\)
- Third multiple: \(3(x + 2) = 3 \times 9 = 27\)

6. **Identify the Largest Number**:
Among the three multiples (21, 24, and 27), the largest number is:
\[ 27 \]

### Final Answer:
The largest number among the three consecutive multiples of 3 that sum to 72 is **27**.

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