If `(7)/(3)%` of a number is 42, then the number is

Options

A. 9800
B. 8
C. 1800
D. 180

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Understand the problem
We need to find a number \( x \) such that \( \frac{7}{3}\% \) of \( x \) equals 42.

### Step 2: Write the equation
We can express the statement "7/3 percent of a number" mathematically. We know that "percent" means "per hundred," so we can write:
\[ \frac{7}{3}\% \text{ of } x = 42 \]
This can be rewritten as:
\[ \frac{7}{3} \times \frac{x}{100} = 42 \]

### Step 3: Simplify the equation
To eliminate the fraction, we can multiply both sides of the equation by 100:
\[ \frac{7}{3} \times x = 42 \times 100 \]
This simplifies to:
\[ \frac{7}{3} \times x = 4200 \]

### Step 4: Solve for \( x \)
Now, we need to isolate \( x \). To do this, we can multiply both sides by the reciprocal of \( \frac{7}{3} \), which is \( \frac{3}{7} \):
\[ x = 4200 \times \frac{3}{7} \]

### Step 5: Calculate \( x \)
Now, we can perform the multiplication:
\[ x = 4200 \times \frac{3}{7} \]
First, divide 4200 by 7:
\[ 4200 \div 7 = 600 \]
Now, multiply by 3:
\[ 600 \times 3 = 1800 \]

### Conclusion
Thus, the number \( x \) is:
\[ \boxed{1800} \]