Find the value of x in each of the following :
x : 1.6 : : 2.1 : 8.4

Answer

To solve the problem \( x : 1.6 :: 2.1 : 8.4 \), we can set up a proportion. This means that the ratio of \( x \) to \( 1.6 \) is equal to the ratio of \( 2.1 \) to \( 8.4 \).

### Step-by-Step Solution:

1. **Set Up the Proportion**:
We can express the given ratio as:
\[ \frac{x}{1.6} = \frac{2.1}{8.4} \]

2. **Cross-Multiply**:
To eliminate the fractions, we can cross-multiply:
\[ x \cdot 8.4 = 1.6 \cdot 2.1 \]

3. **Calculate the Right Side**:
Now, we need to calculate \( 1.6 \cdot 2.1 \):
\[ 1.6 \cdot 2.1 = 3.36 \]

4. **Substitute Back**:
Substitute this value back into the equation:
\[ x \cdot 8.4 = 3.36 \]

5. **Solve for \( x \)**:
Now, divide both sides by \( 8.4 \) to solve for \( x \):
\[ x = \frac{3.36}{8.4} \]

6. **Perform the Division**:
Calculate \( \frac{3.36}{8.4} \):
\[ x = 0.4 \]

### Final Answer:
Thus, the value of \( x \) is \( 0.4 \).

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