What approximate value will come in place of (?) in the following questions ?
`{29.001 + 120.99} div (4.98)^(2) + 4.01 xx (?)^(2) = 75% "of 839.98" + 51.995`

Options

A. 17
B. 13
C. 16
D. 15

Answer

To find the approximate value that will come in place of (?) in the given equation, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the equation with approximate values:**
\[ \{29.001 + 120.99\} \div (4.98)^{2} + 4.01 \times (?)^{2} = 75\% \text{ of } 839.98 + 51.995 \]
Approximate the values:
- \(29.001 \approx 29\)
- \(120.99 \approx 121\)
- \(4.98 \approx 5\)
- \(75\% \text{ of } 839.98 \approx 75\% \text{ of } 840 \approx 630\)
- \(51.995 \approx 52\)

So, the equation becomes:
\[ \{29 + 121\} \div (5)^{2} + 4 \times (?)^{2} = 630 + 52 \]

2. **Calculate the left side:**
- First, calculate the sum in the brackets:
\[ 29 + 121 = 150 \]
- Now, calculate \(5^{2}\):
\[ 5^{2} = 25 \]
- Now, divide:
\[ 150 \div 25 = 6 \]
- So, the left side becomes:
\[ 6 + 4 \times (?)^{2} \]

3. **Calculate the right side:**
- Add the two numbers:
\[ 630 + 52 = 682 \]

4. **Set the left side equal to the right side:**
\[ 6 + 4 \times (?)^{2} = 682 \]

5. **Isolate the term with (?):**
- Subtract 6 from both sides:
\[ 4 \times (?)^{2} = 682 - 6 \]
\[ 4 \times (?)^{2} = 676 \]

6. **Divide by 4:**
\[ (?)^{2} = \frac{676}{4} \]
\[ (?)^{2} = 169 \]

7. **Take the square root:**
\[ ? = \sqrt{169} = 13 \]

### Final Answer:
The approximate value that will come in place of (?) is **13**.

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