The number to be added to each of the numbers 7, 16, 43, 79 to make the numbers in proportion is

Options

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

Answer

To solve the problem of finding the number \( x \) that needs to be added to each of the numbers 7, 16, 43, and 79 so that they are in proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Proportion**:
We want to find \( x \) such that:
\[ \frac{7 + x}{16 + x} = \frac{43 + x}{79 + x} \]

2. **Cross-Multiply**:
To eliminate the fractions, we can cross-multiply:
\[ (7 + x)(79 + x) = (16 + x)(43 + x) \]

3. **Expand Both Sides**:
Now we will expand both sides of the equation:
- Left Side:
\[ 7 \cdot 79 + 7x + 79x + x^2 = 553 + 86x + x^2 \]
- Right Side:
\[ 16 \cdot 43 + 16x + 43x + x^2 = 688 + 59x + x^2 \]

4. **Simplify the Equation**:
Now we can simplify the equation by subtracting \( x^2 \) from both sides:
\[ 553 + 86x = 688 + 59x \]

5. **Rearrange the Equation**:
Next, we will move all terms involving \( x \) to one side and constant terms to the other:
\[ 86x - 59x = 688 - 553 \]
\[ 27x = 135 \]

6. **Solve for \( x \)**:
Finally, we can solve for \( x \):
\[ x = \frac{135}{27} = 5 \]

### Final Answer:
The number to be added to each of the numbers 7, 16, 43, and 79 to make them in proportion is \( \boxed{5} \).