The sum of three consecutive multiples of `8` is `888`. Find the multiples.

Options

A. `248,256,264`
B. `216,224,232`
C. `288,296,304`
D. None

Explanation

To solve the problem of finding three consecutive multiples of 8 that sum to 888, we can follow these steps:

### Step 1: Define the Variables
Let the first multiple of 8 be represented as \( 8k \), where \( k \) is an integer.

### Step 2: Express the Consecutive Multiples
The next two consecutive multiples of 8 can be expressed as:
- Second multiple: \( 8(k + 1) = 8k + 8 \)
- Third multiple: \( 8(k + 2) = 8k + 16 \)

### Step 3: Set Up the Equation
According to the problem, the sum of these three consecutive multiples is 888. Therefore, we can write the equation:
\[ 8k + (8k + 8) + (8k + 16) = 888 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 8k + 8k + 8 + 8k + 16 = 888 \]
This simplifies to:
\[ 24k + 24 = 888 \]

### Step 5: Solve for \( k \)
Now, isolate \( k \) by first subtracting 24 from both sides:
\[ 24k = 888 - 24 \]
\[ 24k = 864 \]
Now, divide both sides by 24:
\[ k = \frac{864}{24} = 36 \]

### Step 6: Find the Multiples
Now that we have \( k = 36 \), we can find the three consecutive multiples of 8:
1. First multiple: \( 8k = 8 \times 36 = 288 \)
2. Second multiple: \( 8(k + 1) = 8 \times 37 = 296 \)
3. Third multiple: \( 8(k + 2) = 8 \times 38 = 304 \)

### Step 7: Conclusion
The three consecutive multiples of 8 that sum to 888 are:
- 288
- 296
- 304