`105.27% "of" 1200.11+11.80% "of" 2360.85=21.99% "of" ? +1420.99`

Options

A. 500
B. 240
C. 310
D. 550

Explanation

To solve the equation \( 105.27\% \text{ of } 1200.11 + 11.80\% \text{ of } 2360.85 = 21.99\% \text{ of } ? + 1420.99 \), we will follow these steps:

### Step 1: Approximate the percentages and values
- Round \( 105.27\% \) to \( 105\% \) (or \( 106\% \) for simplicity).
- Round \( 1200.11 \) to \( 1200 \).
- Round \( 11.80\% \) to \( 12\% \).
- Round \( 2360.85 \) to \( 2361 \).
- Round \( 21.99\% \) to \( 22\% \).
- Round \( 1420.99 \) to \( 1421 \).

### Step 2: Rewrite the equation with approximations
The equation becomes:
\[ 105\% \text{ of } 1200 + 12\% \text{ of } 2361 = 22\% \text{ of } ? + 1421 \]

### Step 3: Calculate the left-hand side
- Calculate \( 105\% \text{ of } 1200 \):
\[ 105\% \text{ of } 1200 = \frac{105}{100} \times 1200 = 1260 \]

- Calculate \( 12\% \text{ of } 2361 \):
\[ 12\% \text{ of } 2361 = \frac{12}{100} \times 2361 = 283.32 \approx 283.2 \]

### Step 4: Combine the results from the left-hand side
\[ 1260 + 283.2 = 1543.2 \]

### Step 5: Set up the right-hand side
The equation now looks like:
\[ 1543.2 = 22\% \text{ of } ? + 1421 \]

### Step 6: Isolate the term with the question mark
Subtract \( 1421 \) from both sides:
\[ 1543.2 - 1421 = 22\% \text{ of } ? \]
\[ 122.2 = 22\% \text{ of } ? \]

### Step 7: Solve for the question mark
Convert \( 22\% \) to a fraction:
\[ 22\% = \frac{22}{100} \]
So we have:
\[ 122.2 = \frac{22}{100} \times ? \]
To isolate \( ? \), multiply both sides by \( \frac{100}{22} \):
\[ ? = \frac{122.2 \times 100}{22} \]
Calculating this gives:
\[ ? = \frac{12220}{22} = 555.45 \]

### Conclusion
The value of \( ? \) is approximately \( 555.45 \).