If `20%` of `(x)/(4)` is `(9)/(10)`, then find the value of x.

Options

A. 18
B. 20
C. 21
D. 25

Answer

To solve the equation where \( 20\% \) of \( \frac{x}{4} \) is equal to \( \frac{9}{10} \), we will follow these steps:

### Step 1: Convert the percentage to a fraction
We know that \( 20\% \) can be expressed as \( \frac{20}{100} \) or \( \frac{1}{5} \).

### Step 2: Set up the equation
The statement "20% of \( \frac{x}{4} \) is \( \frac{9}{10} \)" can be written as:
\[ \frac{20}{100} \times \frac{x}{4} = \frac{9}{10} \]
This simplifies to:
\[ \frac{1}{5} \times \frac{x}{4} = \frac{9}{10} \]

### Step 3: Simplify the left side
Now, we can simplify the left side:
\[ \frac{x}{20} = \frac{9}{10} \]

### Step 4: Cross-multiply
To eliminate the fractions, we can cross-multiply:
\[ x \times 10 = 9 \times 20 \]
This gives us:
\[ 10x = 180 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 10 to isolate \( x \):
\[ x = \frac{180}{10} \]
Thus,
\[ x = 18 \]

### Final Answer
The value of \( x \) is \( 18 \).

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