What number should be added toeach of the numbers 94 ,24, 100 and 26 so that the resulting numbers are in continued proprotion

Options

A. 10
B. 11
C. 9
D. 8

Answer

To solve the problem of finding the number that should be added to each of the numbers 94, 24, 100, and 26 so that the resulting numbers are in continued proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Unknown**:
Let the number to be added be \( x \).

2. **Write the New Numbers**:
The new numbers after adding \( x \) to each will be:
- \( 94 + x \)
- \( 24 + x \)
- \( 100 + x \)
- \( 26 + x \)

3. **Set Up the Continued Proportion**:
For the numbers to be in continued proportion, the following relationship must hold:
\[ \frac{94 + x}{24 + x} = \frac{100 + x}{26 + x} \]

4. **Cross Multiply**:
Cross multiplying gives us:
\[ (94 + x)(26 + x) = (24 + x)(100 + x) \]

5. **Expand Both Sides**:
Expanding both sides:
- Left Side:
\[ 94 \cdot 26 + 94x + 26x + x^2 = 2444 + 120x + x^2 \]
- Right Side:
\[ 24 \cdot 100 + 24x + 100x + x^2 = 2400 + 124x + x^2 \]

6. **Set the Equation**:
Now we set the two expanded sides equal to each other:
\[ 2444 + 120x + x^2 = 2400 + 124x + x^2 \]

7. **Cancel \( x^2 \) from Both Sides**:
Since \( x^2 \) appears on both sides, we can cancel it out:
\[ 2444 + 120x = 2400 + 124x \]

8. **Rearrange the Equation**:
Rearranging gives:
\[ 2444 - 2400 = 124x - 120x \]
\[ 44 = 4x \]

9. **Solve for \( x \)**:
Dividing both sides by 4:
\[ x = 11 \]

10. **Conclusion**:
Therefore, the number that should be added to each of the numbers is \( \boxed{11} \).