If the sum of two numbers, one of which is `(2)/(5)` times the other, is 50, then the numbers are

Options

A. `(115)/(7) and (235)/(7)`
B. `(150)/(7) and (200)/(7)`
C. `(240)/(7) and (110)/(7)`
D. `(250)/(7) and (100)/(7)`

Answer

To solve the problem, we need to find two numbers where one number is \( \frac{2}{5} \) times the other, and their sum is 50. Let's denote the two numbers as \( x \) and \( y \).

### Step-by-Step Solution:

1. **Define the Variables**:
Let \( x \) be the first number and \( y \) be the second number.

2. **Set Up the Equations**:
According to the problem, we have two pieces of information:
- The sum of the two numbers is 50:
\[ x + y = 50 \quad \text{(Equation 1)} \]
- One number is \( \frac{2}{5} \) times the other. We can express this as:
\[ x = \frac{2}{5}y \quad \text{(Equation 2)} \]

3. **Substitute Equation 2 into Equation 1**:
We can substitute \( x \) from Equation 2 into Equation 1:
\[ \frac{2}{5}y + y = 50 \]

4. **Combine Like Terms**:
To combine the terms on the left side, we need a common denominator:
\[ \frac{2}{5}y + \frac{5}{5}y = 50 \]
This simplifies to:
\[ \frac{7}{5}y = 50 \]

5. **Solve for \( y \)**:
To isolate \( y \), multiply both sides by \( \frac{5}{7} \):
\[ y = 50 \times \frac{5}{7} = \frac{250}{7} \]

6. **Find \( x \)**:
Now that we have \( y \), we can find \( x \) using Equation 2:
\[ x = \frac{2}{5}y = \frac{2}{5} \times \frac{250}{7} = \frac{500}{35} = \frac{100}{7} \]

7. **Final Answer**:
The two numbers are:
\[ x = \frac{100}{7}, \quad y = \frac{250}{7} \]

### Summary:
The two numbers are \( \frac{100}{7} \) and \( \frac{250}{7} \).