Find the value of `2.1 + 2.25 div [ 63 - {7.5 xx 8 + (13- 2. 5 xx 5) }].`

Options

A. `2.8`
B. `2.9`
C. `3.0`
D. `4.3`

Answer

To solve the expression \( 2.1 + \frac{2.25}{[63 - \{7.5 \times 8 + (13 - 2.5 \times 5)\}]} \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the innermost parentheses**:
- Calculate \( 2.5 \times 5 \):
\[ 2.5 \times 5 = 12.5 \]
- Substitute back into the expression:
\[ 2.1 + \frac{2.25}{[63 - \{7.5 \times 8 + (13 - 12.5)\}]} \]

2. **Calculate \( 13 - 12.5 \)**:
\[ 13 - 12.5 = 0.5 \]
- Substitute back:
\[ 2.1 + \frac{2.25}{[63 - \{7.5 \times 8 + 0.5\}]} \]

3. **Calculate \( 7.5 \times 8 \)**:
\[ 7.5 \times 8 = 60 \]
- Substitute back:
\[ 2.1 + \frac{2.25}{[63 - (60 + 0.5)]} \]

4. **Calculate \( 60 + 0.5 \)**:
\[ 60 + 0.5 = 60.5 \]
- Substitute back:
\[ 2.1 + \frac{2.25}{[63 - 60.5]} \]

5. **Calculate \( 63 - 60.5 \)**:
\[ 63 - 60.5 = 2.5 \]
- Substitute back:
\[ 2.1 + \frac{2.25}{2.5} \]

6. **Calculate \( \frac{2.25}{2.5} \)**:
\[ \frac{2.25}{2.5} = 0.9 \]
- Substitute back:
\[ 2.1 + 0.9 \]

7. **Calculate \( 2.1 + 0.9 \)**:
\[ 2.1 + 0.9 = 3.0 \]

### Final Answer:
The value of the expression is \( 3.0 \).