The difference between the 38% of a number and 22% of that number is 3200. What is the `15 1/2%` of that number ?

Options

A. 3100
B. 3200
C. 3000
D. 2800

Answer

To solve the problem step by step, let's follow the reasoning laid out in the video transcript.

### Step 1: Define the variable
Let the unknown number be represented as \( x \).

### Step 2: Set up the equation
According to the problem, the difference between 38% of \( x \) and 22% of \( x \) is equal to 3200. We can express this mathematically as:
\[ 0.38x - 0.22x = 3200 \]

### Step 3: Simplify the equation
Now, simplify the left-hand side:
\[ (0.38 - 0.22)x = 3200 \]
\[ 0.16x = 3200 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides by 0.16:
\[ x = \frac{3200}{0.16} \]

Calculating the right-hand side:
\[ x = 3200 \div 0.16 = 20000 \]

### Step 5: Calculate 15.5% of \( x \)
Now, we need to find \( 15.5\% \) of \( x \):
\[ 15.5\% = \frac{15.5}{100} = \frac{31}{200} \]
So,
\[ 15.5\% \text{ of } x = \frac{31}{200} \times 20000 \]

### Step 6: Perform the multiplication
Calculating this gives:
\[ = 31 \times 100 = 3100 \]

### Conclusion
Thus, \( 15.5\% \) of the number is:
\[ \boxed{3100} \]