Find a if 3,a,7,28` are in proportion.

Answer

To find the value of \( a \) in the proportion \( 3, a, 7, 28 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Proportion**:
When four numbers \( a, b, c, d \) are in proportion, it means that \( \frac{a}{b} = \frac{c}{d} \). In our case, we have \( 3, a, 7, 28 \). Therefore, we can write:
\[ \frac{3}{a} = \frac{7}{28} \]

2. **Cross Multiplying**:
To eliminate the fractions, we can cross-multiply:
\[ 3 \times 28 = a \times 7 \]
This simplifies to:
\[ 84 = 7a \]

3. **Isolating \( a \)**:
To find \( a \), we need to isolate it. We do this by dividing both sides of the equation by 7:
\[ a = \frac{84}{7} \]

4. **Calculating the Value**:
Now, we perform the division:
\[ a = 12 \]

5. **Final Answer**:
Thus, the value of \( a \) is \( 12 \).

### Verification:
To verify our solution, we can check if the ratios are equal:
\[ \frac{3}{12} = \frac{7}{28} \]
Calculating both sides:
- The left side simplifies to \( \frac{1}{4} \).
- The right side simplifies to \( \frac{1}{4} \).

Since both sides are equal, our solution is confirmed.