The sum of two consecutive multiples of `3` is `69`. Find them.

Options

A. `33 and 34`
B. `31 and 35`
C. `33 and 36`
D. none of these

Answer

To solve the problem of finding two consecutive multiples of 3 that sum up to 69, we can follow these steps:

### Step 1: Define the Variables
Let the first multiple of 3 be represented as \( x \). Since we are looking for consecutive multiples of 3, the next consecutive multiple of 3 can be expressed as \( x + 3 \).

### Step 2: Set Up the Equation
According to the problem, the sum of these two consecutive multiples of 3 is 69. Therefore, we can write the equation:
\[ x + (x + 3) = 69 \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ x + x + 3 = 69 \]
This simplifies to:
\[ 2x + 3 = 69 \]

### Step 4: Isolate the Variable
Next, we need to isolate \( x \). Start by subtracting 3 from both sides:
\[ 2x = 69 - 3 \]
This simplifies to:
\[ 2x = 66 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{66}{2} \]
This gives us:
\[ x = 33 \]

### Step 6: Find the Consecutive Multiples
Now that we have \( x \), we can find the two consecutive multiples of 3:
- The first multiple is \( 3x = 3 \times 33 = 99 \).
- The second multiple is \( 3x + 3 = 3 \times 33 + 3 = 99 + 3 = 102 \).

### Final Answer
The two consecutive multiples of 3 that sum to 69 are:
- First multiple: 33
- Second multiple: 36