Find the value of x in each of the following :
1 . 8 : x : : 2 . 4 : 6 . 0

Answer

To find the value of \( x \) in the ratio \( 1.8 : x :: 2.4 : 6.0 \), we can set up a proportion based on the given ratios.

### Step-by-Step Solution:

1. **Set up the proportion**:
The expression \( 1.8 : x :: 2.4 : 6.0 \) can be written as:
\[ \frac{1.8}{x} = \frac{2.4}{6.0} \]

2. **Cross-multiply**:
To eliminate the fractions, we can cross-multiply:
\[ 1.8 \times 6.0 = 2.4 \times x \]

3. **Calculate \( 1.8 \times 6.0 \)**:
Now, we calculate the left side:
\[ 1.8 \times 6.0 = 10.8 \]

4. **Set up the equation**:
Now we have:
\[ 10.8 = 2.4 \times x \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides by \( 2.4 \):
\[ x = \frac{10.8}{2.4} \]

6. **Calculate \( \frac{10.8}{2.4} \)**:
Performing the division:
\[ x = 4.5 \]

### Final Answer:
Thus, the value of \( x \) is \( 4.5 \).

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