16% of `550 div ?% ` of 500=2.5

Options

A. 5.64
B. 8.11
C. 7.04
D. 6.08

Explanation

To solve the equation \( 16\% \text{ of } 550 \div ?\% \text{ of } 500 = 2.5 \), we will follow these steps:

### Step 1: Convert percentages to fractions
First, we convert the percentages into fractions:
- \( 16\% = \frac{16}{100} \)
- Let \( x\% = \frac{x}{100} \)

### Step 2: Write the equation
The equation can be rewritten as:
\[ \frac{16}{100} \times 550 \div \left(\frac{x}{100} \times 500\right) = 2.5 \]

### Step 3: Simplify the equation
Now, we simplify the left side:
\[ \frac{16 \times 550}{100} \div \left(\frac{x \times 500}{100}\right) = 2.5 \]

This can be simplified to:
\[ \frac{16 \times 550}{100} \times \frac{100}{x \times 500} = 2.5 \]

### Step 4: Cancel out the common terms
The \( 100 \) in the numerator and denominator cancels out:
\[ \frac{16 \times 550}{x \times 500} = 2.5 \]

### Step 5: Cross-multiply
Now, we cross-multiply to eliminate the fraction:
\[ 16 \times 550 = 2.5 \times x \times 500 \]

### Step 6: Calculate \( 16 \times 550 \)
Calculating \( 16 \times 550 \):
\[ 16 \times 550 = 8800 \]

### Step 7: Substitute back into the equation
Now substitute back into the equation:
\[ 8800 = 2.5 \times x \times 500 \]

### Step 8: Simplify the right side
Calculating \( 2.5 \times 500 \):
\[ 2.5 \times 500 = 1250 \]
So the equation becomes:
\[ 8800 = 1250x \]

### Step 9: Solve for \( x \)
Now, divide both sides by \( 1250 \):
\[ x = \frac{8800}{1250} \]

### Step 10: Calculate the division
Calculating \( \frac{8800}{1250} \):
\[ x = 7.04 \]

### Final Answer
Thus, the value of \( ? \) is \( 7.04 \).

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