The sum of two positive integrs in 34 and their difference is 8. Find their product.

Options

A. 308
B. 273
C. 209
D. 345

Answer

To solve the problem step by step, we need to find two positive integers whose sum is 34 and whose difference is 8. Let's denote these two integers as A and B.

### Step 1: Set up the equations
From the problem, we have two equations based on the information provided:
1. \( A + B = 34 \) (Equation 1: The sum of the two integers)
2. \( A - B = 8 \) (Equation 2: The difference of the two integers)

### Step 2: Solve the equations
To solve for A and B, we can add both equations together to eliminate B:
\[ (A + B) + (A - B) = 34 + 8 \]
This simplifies to:
\[ 2A = 42 \]
Now, divide both sides by 2 to find A:
\[ A = 21 \]

### Step 3: Substitute A back to find B
Now that we have A, we can substitute it back into Equation 1 to find B:
\[ 21 + B = 34 \]
Subtract 21 from both sides:
\[ B = 34 - 21 \]
\[ B = 13 \]

### Step 4: Find the product of A and B
Now that we have both integers, A = 21 and B = 13, we can find their product:
\[ A \times B = 21 \times 13 \]
Calculating this:
\[ 21 \times 13 = 273 \]

### Conclusion
The product of the two integers is \( 273 \).

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