`56% "of" 4356 = 76% "of" 564+?`

Options

A. 1789
B. 2100
C. 2500
D. 2011

Explanation

To solve the equation \( 56\% \text{ of } 4356 = 76\% \text{ of } 564 + ? \), we will follow these steps:

### Step 1: Convert percentages to decimals and set up the equation
We start by rewriting the percentages as decimals:
\[ 56\% = \frac{56}{100} \quad \text{and} \quad 76\% = \frac{76}{100} \]
Thus, we can express the equation as:
\[ \frac{56}{100} \times 4356 = \frac{76}{100} \times 564 + x \]

### Step 2: Calculate \( 56\% \text{ of } 4356 \)
Now we calculate \( 56\% \text{ of } 4356 \):
\[ \frac{56}{100} \times 4356 = 0.56 \times 4356 = 2433.36 \]

### Step 3: Calculate \( 76\% \text{ of } 564 \)
Next, we calculate \( 76\% \text{ of } 564 \):
\[ \frac{76}{100} \times 564 = 0.76 \times 564 = 427.84 \]

### Step 4: Substitute the values back into the equation
Now we substitute the calculated values back into the equation:
\[ 2433.36 = 427.84 + x \]

### Step 5: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = 2433.36 - 427.84 \]
Calculating this gives:
\[ x = 2005.52 \]

### Step 6: Round the result
Finally, we round \( 2005.52 \) to the nearest whole number:
\[ x \approx 2006 \]

Thus, the final answer is:
\[ \boxed{2006} \]