A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?

Options

A. 6
B. 3.5
C. 8
D. None of these

Answer

To solve the problem step by step, let's define the unknown number as \( x \).

### Step 1: Set up the equation
According to the problem, when the number \( x \) is doubled and then 9 is added, we can express this as:
\[ 2x + 9 \]

### Step 2: Treble the resultant
The problem states that this resultant is then trebled (multiplied by 3), which gives us:
\[ 3(2x + 9) \]

### Step 3: Set the equation equal to 75
We know from the problem that this final result equals 75:
\[ 3(2x + 9) = 75 \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
\[ 2x + 9 = \frac{75}{3} \]
Calculating the right side:
\[ 2x + 9 = 25 \]

### Step 5: Solve for \( 2x \)
Next, we isolate \( 2x \) by subtracting 9 from both sides:
\[ 2x = 25 - 9 \]
Calculating the right side:
\[ 2x = 16 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{16}{2} \]
Calculating the right side:
\[ x = 8 \]

### Conclusion
Thus, the number is:
\[ \boxed{8} \]