If `x : 18 :: 5 : 3` find the value of x.

Answer

To solve the problem where \( x : 18 :: 5 : 3 \), we can set up a proportion based on the given ratios.

### Step-by-Step Solution:

1. **Set up the proportion**:
The statement \( x : 18 :: 5 : 3 \) means that the ratio \( \frac{x}{18} \) is equal to the ratio \( \frac{5}{3} \). Therefore, we can write:
\[ \frac{x}{18} = \frac{5}{3} \]

2. **Cross-multiply**:
To eliminate the fractions, we can cross-multiply:
\[ x \cdot 3 = 5 \cdot 18 \]

3. **Calculate the right side**:
Now, calculate \( 5 \cdot 18 \):
\[ 5 \cdot 18 = 90 \]
So, we have:
\[ 3x = 90 \]

4. **Solve for \( x \)**:
To isolate \( x \), divide both sides by 3:
\[ x = \frac{90}{3} \]

5. **Calculate the final value**:
Now, perform the division:
\[ x = 30 \]

Thus, the value of \( x \) is \( 30 \).