The product of two positive numbers is 2500. If one number is four times the other, then the sum of the two numbers is

Options

A. 25
B. 125
C. 225
D. 250

Answer

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

### Step 1: Define the Variables
Let the two positive numbers be \( x \) and \( y \). According to the problem, one number is four times the other. We can express this relationship as:
\[ x = 4y \]

### Step 2: Use the Product Condition
We know that the product of the two numbers is 2500. Therefore, we can write the equation:
\[ x \cdot y = 2500 \]

### Step 3: Substitute the Value of \( x \)
Now, substitute \( x \) from Step 1 into the product equation:
\[ (4y) \cdot y = 2500 \]
This simplifies to:
\[ 4y^2 = 2500 \]

### Step 4: Solve for \( y \)
To find \( y \), divide both sides of the equation by 4:
\[ y^2 = \frac{2500}{4} \]
\[ y^2 = 625 \]
Now, take the square root of both sides:
\[ y = \sqrt{625} \]
\[ y = 25 \]

### Step 5: Find \( x \)
Now that we have \( y \), we can find \( x \) using the relationship defined in Step 1:
\[ x = 4y = 4 \cdot 25 = 100 \]

### Step 6: Calculate the Sum of \( x \) and \( y \)
Finally, we can find the sum of the two numbers:
\[ x + y = 100 + 25 = 125 \]

### Conclusion
The sum of the two numbers is \( 125 \).

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