Two numbers are in the ratio `3:7` and their sum is 230. Find the numbers.

Answer

To solve the problem of finding two numbers that are in the ratio of 3:7 and whose sum is 230, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The two numbers are in the ratio of 3:7. This means that if we let the first number be \(3x\), then the second number will be \(7x\), where \(x\) is a common multiplier.

2. **Set Up the Equation**: According to the problem, the sum of these two numbers is 230. Therefore, we can write the equation:
\[ 3x + 7x = 230 \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ 10x = 230 \]

4. **Solve for \(x\)**: To find the value of \(x\), divide both sides of the equation by 10:
\[ x = \frac{230}{10} = 23 \]

5. **Find the Two Numbers**: Now that we have the value of \(x\), we can find the two numbers:
- The first number is:
\[ 3x = 3 \times 23 = 69 \]
- The second number is:
\[ 7x = 7 \times 23 = 161 \]

6. **Conclusion**: The two numbers are 69 and 161.

### Final Answer:
The two numbers are **69** and **161**.

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