Question

If \(x > 0\), then which of the following expressions are equal to 3.6% of \(\frac{5x}{12}\) ? 
A. 3 percent of 20x 
B. x percent of \(\frac{3}{2}\)
C. 3x percent of 0.2 
D. 0.05 percent of 3x
E. \(\frac{3x}{200}\)
Choose the correct answer from the options given below:

• A. A and B only
• B. A and E only
• C. C and D only
• D. B and E only

Answer 1

The Correct Option is D

To determine which expressions are equal to 3.6% of \(\frac{5x}{12}\), we need to calculate this value and compare it with each option.

First, compute 3.6% of \(\frac{5x}{12}\):

3.6\% of \(\frac{5x}{12}\) is calculated as:

\(\frac{3.6}{100} \times \frac{5x}{12} = \frac{18}{500} \times \frac{5x}{12} = \frac{90x}{6000} = \frac{3x}{200}\)

So, we need to identify which options result in \(\frac{3x}{200}\).

Let’s evaluate each option step-by-step:

1. **Option A: 3 percent of 20x** \(\frac{3}{100} \times 20x = \frac{60x}{100} = \frac{3x}{5}\)
   This is not equal to \(\frac{3x}{200}\).
2. **Option B: x percent of \(\frac{3}{2}\)** \(\frac{x}{100} \times \frac{3}{2} = \frac{3x}{200}\)
   This matches \(\frac{3x}{200}\).
3. **Option C: 3x percent of 0.2** \(\frac{3x}{100} \times 0.2 = \frac{0.6x}{100} = \frac{3x}{500}\)
   This is not equal to \(\frac{3x}{200}\).
4. **Option D: 0.05 percent of 3x** \(\frac{0.05}{100} \times 3x = \frac{0.15x}{10000} = \frac{3x}{200000}\)
   This is not equal to \(\frac{3x}{200}\).
5. **Option E: \(\frac{3x}{200}\)**
   Strictly given as \(\frac{3x}{200}\), which is exactly what we computed.

Therefore, the expressions that are equal to 3.6% of \(\frac{5x}{12}\) are found in B and E only.