If 30% of 40% of X is 240, then what is the value of X?

Options

A. 441
B. 2000
C. 1200
D. 1800

Answer

To solve the equation "If 30% of 40% of X is 240, then what is the value of X?", we can follow these steps:

### Step 1: Convert percentages to fractions
We know that:
- 30% can be expressed as \( \frac{30}{100} = \frac{3}{10} \)
- 40% can be expressed as \( \frac{40}{100} = \frac{2}{5} \)

### Step 2: Set up the equation
We can express the problem as:
\[ 30\% \text{ of } 40\% \text{ of } X = 240 \]
This can be rewritten using the fractions:
\[ \frac{3}{10} \times \frac{2}{5} \times X = 240 \]

### Step 3: Simplify the left side
Now, we can multiply the fractions:
\[ \frac{3 \times 2}{10 \times 5} \times X = 240 \]
This simplifies to:
\[ \frac{6}{50} \times X = 240 \]
We can further simplify \( \frac{6}{50} \) to \( \frac{3}{25} \):
\[ \frac{3}{25} \times X = 240 \]

### Step 4: Solve for X
To isolate X, we can multiply both sides by the reciprocal of \( \frac{3}{25} \), which is \( \frac{25}{3} \):
\[ X = 240 \times \frac{25}{3} \]

### Step 5: Calculate the value of X
Now, we can perform the multiplication:
\[ X = \frac{240 \times 25}{3} \]
Calculating \( 240 \div 3 = 80 \):
\[ X = 80 \times 25 = 2000 \]

### Final Answer
Thus, the value of \( X \) is \( 2000 \).

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