`8 (2)/(7) "of" 1568 +265.75 =? + 2455.60`

Options

A. `10354.15`
B. `10578.15`
C. `10802.15`
D. `11250.15`

Answer

To solve the equation \( 8 \frac{2}{7} \text{ of } 1568 + 265.75 = ? + 2455.60 \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 8 \frac{2}{7} \) can be converted to an improper fraction.

\[ 8 \frac{2}{7} = \frac{(8 \times 7) + 2}{7} = \frac{56 + 2}{7} = \frac{58}{7} \]

**Hint:** To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place it over the original denominator.

### Step 2: Calculate \( \frac{58}{7} \text{ of } 1568 \)
Now, we need to calculate \( \frac{58}{7} \times 1568 \).

\[ \frac{58}{7} \times 1568 = \frac{58 \times 1568}{7} \]

Calculating \( 58 \times 1568 \):

\[ 58 \times 1568 = 9104 \]

Now divide by 7:

\[ \frac{9104}{7} = 1300.57142857 \approx 1300.57 \text{ (rounded to two decimal places)} \]

**Hint:** When multiplying fractions, multiply the numerators together and the denominators together. Then simplify if possible.

### Step 3: Add \( 265.75 \) to the result
Now, we add \( 265.75 \) to \( 1300.57 \):

\[ 1300.57 + 265.75 = 1566.32 \]

**Hint:** When adding decimals, align the decimal points to ensure accurate addition.

### Step 4: Set up the equation
Now we have:

\[ 1566.32 = ? + 2455.60 \]

### Step 5: Solve for \( ? \)
To find \( ? \), we need to isolate it:

\[ ? = 1566.32 - 2455.60 \]

Calculating this gives:

\[ ? = -889.28 \]

**Hint:** To isolate a variable, perform the opposite operation. Here, we subtracted \( 2455.60 \) from both sides.

### Final Answer
Thus, the solution to the equation is:

\[ ? = -889.28 \]