Which of the following numbers should be added to 11, 15, 17 and 23 so that they are in proportion?

Options

A. 2
B. 3
C. 5
D. 1

Answer

To solve the problem of determining which number should be added to 11, 15, 17, and 23 so that they are in proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
Let the number to be added be \( x \). We need to set up the proportion:
\[ \frac{11 + x}{15 + x} = \frac{17 + x}{23 + x} \]

2. **Cross Multiply**:
To eliminate the fractions, we can cross multiply:
\[ (11 + x)(23 + x) = (15 + x)(17 + x) \]

3. **Expand Both Sides**:
Expanding both sides gives:
\[ 11 \cdot 23 + 11x + 23x + x^2 = 15 \cdot 17 + 15x + 17x + x^2 \]
Simplifying this, we have:
\[ 253 + 34x + x^2 = 255 + 32x + x^2 \]

4. **Cancel \( x^2 \)**:
Since \( x^2 \) appears on both sides, we can cancel it out:
\[ 253 + 34x = 255 + 32x \]

5. **Rearrange the Equation**:
Now, rearranging the equation gives:
\[ 34x - 32x = 255 - 253 \]
Simplifying this results in:
\[ 2x = 2 \]

6. **Solve for \( x \)**:
Dividing both sides by 2 gives:
\[ x = 1 \]

7. **Conclusion**:
Therefore, the number that should be added to 11, 15, 17, and 23 to make them proportional is \( x = 1 \).

### Final Answer:
The number that should be added is **1**.