The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.

Options

A. 112
B. 126
C. 119
D. 116

Answer

To solve the problem of finding the smallest multiple of 7 among three consecutive multiples that sum to 357, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Variables**:
Let's denote the first multiple of 7 as \(7x\). The next two consecutive multiples of 7 can then be expressed as:
- First multiple: \(7x\)
- Second multiple: \(7x + 7\)
- Third multiple: \(7x + 14\)

2. **Set Up the Equation**:
According to the problem, the sum of these three multiples is equal to 357. Therefore, we can write the equation:
\[ 7x + (7x + 7) + (7x + 14) = 357 \]

3. **Combine Like Terms**:
Now, let's simplify the left side of the equation:
\[ 7x + 7x + 7 + 7x + 14 = 357 \]
This simplifies to:
\[ 21x + 21 = 357 \]

4. **Isolate the Variable**:
Next, we need to isolate \(21x\) by subtracting 21 from both sides:
\[ 21x = 357 - 21 \]
Simplifying the right side gives:
\[ 21x = 336 \]

5. **Solve for \(x\)**:
Now, divide both sides by 21 to find \(x\):
\[ x = \frac{336}{21} \]
Performing the division:
\[ x = 16 \]

6. **Find the Smallest Multiple**:
The smallest multiple of 7 is given by \(7x\). Now that we have \(x\):
\[ 7x = 7 \times 16 = 112 \]

### Final Answer:
The smallest multiple of 7 among the three consecutive multiples is **112**.

---