The sum of two numbers is three times the smaller number and the difference between them is equal to the smaller number. What is definitely the bigger number ?

Options

A. 28
B. 36
C. 39
D. Data inadequate

Answer

To solve the problem, let's define the two numbers. Let the smaller number be \( y \) and the bigger number be \( x \).

### Step 1: Set up the equations based on the problem statement.
1. The sum of the two numbers is three times the smaller number:
\[ x + y = 3y \]
2. The difference between the two numbers is equal to the smaller number:
\[ x - y = y \]

### Step 2: Simplify the equations.
From the first equation:
\[ x + y = 3y \implies x = 3y - y \implies x = 2y \]

From the second equation:
\[ x - y = y \implies x = y + y \implies x = 2y \]

### Step 3: Confirm the equations.
Both equations give us the same result:
\[ x = 2y \]

### Step 4: Find the bigger number.
Since \( x = 2y \), we can conclude that the bigger number is definitely:
\[ x = 2y \]
This means that the bigger number is always twice the smaller number.

### Conclusion
Thus, the bigger number is:
\[ \text{Bigger number} = 2 \times \text{(smaller number)} \]