The sum of two positive integers is 42 and their difference is 4 . Find their product.

Options

A. 402
B. 437
C. 416
D. 376

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variables
Let the two positive integers be \( x \) and \( y \).

### Step 2: Set up the equations
From the problem, we know:
1. The sum of the two integers:
\[ x + y = 42 \quad \text{(Equation 1)} \]
2. The difference of the two integers:
\[ x - y = 4 \quad \text{(Equation 2)} \]

### Step 3: Add the two equations
To eliminate \( y \), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 42 + 4 \]
This simplifies to:
\[ 2x = 46 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 2:
\[ x = \frac{46}{2} = 23 \]

### Step 5: Substitute \( x \) back into Equation 1
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 23 + y = 42 \]
Subtract 23 from both sides:
\[ y = 42 - 23 = 19 \]

### Step 6: Find the product of \( x \) and \( y \)
Now we have both integers \( x = 23 \) and \( y = 19 \). We need to find their product:
\[ x \cdot y = 23 \cdot 19 \]

### Step 7: Calculate the product
To calculate \( 23 \cdot 19 \):
\[ 23 \cdot 19 = 437 \]

### Final Answer
The product of the two integers is \( 437 \).

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