Find two numbers whose sum is 28 and difference is 4. Mark the smaller of them.

Options

A. 10
B. 24
C. 12
D. 4

Explanation

To find the two numbers whose sum is 28 and difference is 4, we can set up the problem using algebraic equations.

### Step 1: Define the Variables
Let the smaller number be \( y \) and the larger number be \( x \).

### Step 2: Set Up the Equations
From the problem, we have two equations based on the information given:
1. The sum of the two numbers:
\[ x + y = 28 \quad \text{(Equation 1)} \]
2. The difference between the two numbers:
\[ x - y = 4 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
To find the values of \( x \) and \( y \), we can use the method of elimination. We will subtract Equation 2 from Equation 1.

Subtract Equation 2 from Equation 1:
\[ (x + y) - (x - y) = 28 - 4 \]
This simplifies to:
\[ x + y - x + y = 24 \]
\[ 2y = 24 \]

### Step 4: Solve for \( y \)
Now, divide both sides by 2:
\[ y = \frac{24}{2} = 12 \]

### Step 5: Find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x + 12 = 28 \]
Subtract 12 from both sides:
\[ x = 28 - 12 = 16 \]

### Conclusion
The two numbers are \( x = 16 \) and \( y = 12 \). The smaller number is \( 12 \).