Find x if `36, 54, 20, x` are in proportion.

Answer

To solve the problem of finding \( x \) when \( 36, 54, 20, x \) are in proportion, 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 the ratio of the first two numbers is equal to the ratio of the last two numbers. Mathematically, this can be expressed as:
\[ \frac{a}{b} = \frac{c}{d} \]

2. **Setting Up the Equation**:
For our problem, we have:
\[ \frac{36}{54} = \frac{20}{x} \]

3. **Cross Multiplying**:
To eliminate the fractions, we can cross multiply:
\[ 36 \cdot x = 20 \cdot 54 \]

4. **Calculating the Right Side**:
Now, we need to calculate \( 20 \cdot 54 \):
\[ 20 \cdot 54 = 1080 \]
So, we have:
\[ 36 \cdot x = 1080 \]

5. **Solving for \( x \)**:
To find \( x \), we divide both sides of the equation by 36:
\[ x = \frac{1080}{36} \]

6. **Calculating \( x \)**:
Now, we simplify \( \frac{1080}{36} \):
\[ x = 30 \]

### Final Answer:
Thus, the value of \( x \) is \( 30 \).

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