Two positive whole numbers are such that the sum of the first number and twice the second number is 8 and their difference is 2. The numbers are :

Options

A. 7,5
B. 6,4
C. 4,2
D. 3,5

Answer

To solve the problem, we need to find two positive whole numbers based on the given conditions. Let's denote the first number as \( x \) and the second number as \( y \).

### Step 1: Set up the equations
From the problem statement, we have two conditions:
1. The sum of the first number and twice the second number is 8:
\[ x + 2y = 8 \quad \text{(Equation 1)} \]
2. The difference between the first number and the second number is 2:
\[ x - y = 2 \quad \text{(Equation 2)} \]

### Step 2: Solve for one variable
From Equation 2, we can express \( x \) in terms of \( y \):
\[ x = y + 2 \quad \text{(Equation 3)} \]

### Step 3: Substitute into the first equation
Now, we substitute Equation 3 into Equation 1:
\[ (y + 2) + 2y = 8 \]

### Step 4: Simplify the equation
Combine like terms:
\[ y + 2 + 2y = 8 \\ 3y + 2 = 8 \]

### Step 5: Solve for \( y \)
Now, isolate \( y \):
\[ 3y = 8 - 2 \\ 3y = 6 \\ y = \frac{6}{3} \\ y = 2 \]

### Step 6: Find \( x \)
Now that we have \( y \), we can find \( x \) using Equation 3:
\[ x = y + 2 \\ x = 2 + 2 \\ x = 4 \]

### Conclusion
The two positive whole numbers are:
- First number \( x = 4 \)
- Second number \( y = 2 \)

### Final Answer
The numbers are 4 and 2.

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