Two-fifths of one-fourth of three-sevenths of a number is 15. What is half of that number?

Options

A. a. 96
B. b. 196
C. c. 94
D. d. None of these

Answer

To solve the problem step by step, we will start by translating the statement into a mathematical equation.

### Step 1: Set up the equation
The problem states that two-fifths of one-fourth of three-sevenths of a number is equal to 15. Let's denote the unknown number as \( x \).

The equation can be set up as follows:
\[ \frac{2}{5} \times \frac{1}{4} \times \frac{3}{7} \times x = 15 \]

### Step 2: Simplify the left side
Now we will simplify the left side of the equation:
\[ \frac{2 \times 1 \times 3}{5 \times 4 \times 7} \times x = 15 \]
Calculating the numerator and denominator:
\[ \frac{6}{140} \times x = 15 \]
We can simplify \(\frac{6}{140}\) to \(\frac{3}{70}\):
\[ \frac{3}{70} \times x = 15 \]

### Step 3: Isolate \( x \)
To isolate \( x \), we will multiply both sides by the reciprocal of \(\frac{3}{70}\):
\[ x = 15 \times \frac{70}{3} \]

### Step 4: Calculate \( x \)
Now we will perform the multiplication:
\[ x = 15 \times \frac{70}{3} = \frac{1050}{3} = 350 \]

### Step 5: Find half of \( x \)
Now that we have found \( x \), we need to find half of that number:
\[ \text{Half of } x = \frac{350}{2} = 175 \]

### Final Answer
Thus, half of the number is:
\[ \boxed{175} \]

---