If `20%` of `x+40%` of `(x)/(2)+20%` of `3x=100`, then find the value of x.

Explanation

To solve the equation \(20\%\) of \(x + 40\%\) of \(\frac{x}{2} + 20\%\) of \(3x = 100\), we will follow these steps:

### Step 1: Convert percentages to fractions
We can convert the percentages to fractions for easier calculations:
- \(20\% = \frac{20}{100} = \frac{1}{5}\)
- \(40\% = \frac{40}{100} = \frac{2}{5}\)

Now, we rewrite the equation:
\[ \frac{1}{5}x + \frac{2}{5}\left(\frac{x}{2}\right) + \frac{1}{5}(3x) = 100 \]

### Step 2: Simplify each term
Now, simplify each term in the equation:
1. The first term is \(\frac{1}{5}x\).
2. The second term is \(\frac{2}{5} \cdot \frac{x}{2} = \frac{2x}{10} = \frac{1}{5}x\).
3. The third term is \(\frac{1}{5}(3x) = \frac{3x}{5}\).

Now, we can combine these terms:
\[ \frac{1}{5}x + \frac{1}{5}x + \frac{3}{5}x = 100 \]

### Step 3: Combine like terms
Combine the \(x\) terms:
\[ \left(\frac{1}{5} + \frac{1}{5} + \frac{3}{5}\right)x = 100 \]
This simplifies to:
\[ \frac{5}{5}x = 100 \]
or simply:
\[ x = 100 \]

### Step 4: Conclusion
Thus, the value of \(x\) is:
\[ \boxed{100} \]