The product of two positive numbers is 1152. If one number is two times the other, what will be the sum of the two numbers?

Options

A. 68
B. 72
C. 76
D. 80

Answer

To solve the problem step by step, let's denote the two positive numbers as \( x \) and \( y \). According to the problem, we have the following information:

1. The product of the two numbers is 1152:
\[ x \cdot y = 1152 \]

2. One number is two times the other:
\[ x = 2y \]

Now, we can substitute the value of \( x \) from the second equation into the first equation.

### Step 1: Substitute \( x \) in the product equation
Substituting \( x = 2y \) into the product equation:
\[ (2y) \cdot y = 1152 \]
This simplifies to:
\[ 2y^2 = 1152 \]

### Step 2: Solve for \( y^2 \)
Now, divide both sides of the equation by 2:
\[ y^2 = \frac{1152}{2} \]
Calculating the right side gives:
\[ y^2 = 576 \]

### Step 3: Find \( y \)
Next, take the square root of both sides to find \( y \):
\[ y = \sqrt{576} \]
Calculating the square root gives:
\[ y = 24 \]

### Step 4: Find \( x \)
Now that we have \( y \), we can find \( x \) using the equation \( x = 2y \):
\[ x = 2 \cdot 24 = 48 \]

### Step 5: Calculate the sum of \( x \) and \( y \)
Finally, we find the sum of the two numbers:
\[ x + y = 48 + 24 = 72 \]

Thus, the sum of the two numbers is:
\[ \boxed{72} \]