Find the value of x in each of the following, so that the numbers are in proportion.
`4, 5, x, 480`

Answer

To find the value of \( x \) in the proportion \( 4, 5, x, 480 \), we can set up the equation based on the property of proportions.

### Step-by-Step Solution:

1. **Understanding Proportions**:
When four numbers \( a, b, c, d \) are in proportion, it means that:
\[ \frac{a}{b} = \frac{c}{d} \]
In our case, we have \( a = 4 \), \( b = 5 \), \( c = x \), and \( d = 480 \).

2. **Setting Up the Equation**:
According to the property of proportions, we can write:
\[ \frac{4}{5} = \frac{x}{480} \]

3. **Cross Multiplying**:
To eliminate the fractions, we can cross multiply:
\[ 4 \times 480 = 5 \times x \]

4. **Calculating the Left Side**:
Now, calculate \( 4 \times 480 \):
\[ 4 \times 480 = 1920 \]
So, we have:
\[ 1920 = 5x \]

5. **Solving for \( x \)**:
To find \( x \), divide both sides by 5:
\[ x = \frac{1920}{5} \]

6. **Calculating the Division**:
Now, perform the division:
\[ x = 384 \]

### Final Answer:
The value of \( x \) is \( 384 \).

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