75% of `(3)/(4) xx (8)/(9) xx 1800 = ? + 600`

Options

A. 300
B. 400
C. 250
D. 480

Answer

To solve the equation \( 75\% \text{ of } \frac{3}{4} \times \frac{8}{9} \times 1800 = ? + 600 \), we can follow these steps:

### Step 1: Convert the percentage to a fraction
We know that \( 75\% \) can be expressed as \( \frac{75}{100} \) or \( \frac{3}{4} \).

### Step 2: Set up the equation
We can rewrite the equation as:
\[ \frac{3}{4} \times \frac{8}{9} \times 1800 = ? + 600 \]

### Step 3: Calculate \( \frac{3}{4} \times \frac{8}{9} \)
First, we multiply \( \frac{3}{4} \) and \( \frac{8}{9} \):
\[ \frac{3 \times 8}{4 \times 9} = \frac{24}{36} = \frac{2}{3} \]

### Step 4: Multiply by 1800
Now, we multiply \( \frac{2}{3} \) by 1800:
\[ \frac{2}{3} \times 1800 = \frac{2 \times 1800}{3} = \frac{3600}{3} = 1200 \]

### Step 5: Substitute back into the equation
Now we substitute back into the equation:
\[ 1200 = ? + 600 \]

### Step 6: Solve for ?
To find \( ? \), we subtract 600 from both sides:
\[ ? = 1200 - 600 = 600 \]

### Final Answer
Thus, the value of \( ? \) is:
\[ ? = 600 \]