Two-third of one-seventh of a number is 87.5% of 240. What is the number?

Options

A. 2670
B. 2450
C. 2205
D. 1470

Answer

To solve the problem step by step, let's break it down clearly.

### Step 1: Understand the Problem
We need to find a number \( x \) such that two-thirds of one-seventh of \( x \) equals 87.5% of 240.

### Step 2: Express the Problem Mathematically
First, we express one-seventh of \( x \):
\[ \text{One-seventh of } x = \frac{1}{7} x \]

Next, we find two-thirds of that:
\[ \text{Two-thirds of } \left(\frac{1}{7} x\right) = \frac{2}{3} \times \frac{1}{7} x = \frac{2}{21} x \]

Now, we need to calculate 87.5% of 240:
\[ 87.5\% \text{ of } 240 = \frac{87.5}{100} \times 240 \]

### Step 3: Calculate 87.5% of 240
To simplify this calculation:
\[ \frac{87.5}{100} \times 240 = 0.875 \times 240 \]
Calculating \( 0.875 \times 240 \):
\[ 0.875 \times 240 = 210 \]

### Step 4: Set Up the Equation
Now we can set up the equation:
\[ \frac{2}{21} x = 210 \]

### Step 5: Solve for \( x \)
To find \( x \), we multiply both sides of the equation by \( \frac{21}{2} \):
\[ x = 210 \times \frac{21}{2} \]

Calculating the right side:
\[ x = 210 \times 10.5 = 2205 \]

### Final Answer
The number \( x \) is:
\[ \boxed{2205} \]