What approximate value will come in place of the question mark (?) in the following questions ? (You are not expected to calculate the exact value.)
`14.89^2-11.16^2+(299.92+350.15)div?=153.85`

Options

A. 18
B. 13
C. 21
D. 16

Answer

To solve the equation \( 14.89^2 - 11.16^2 + (299.92 + 350.15) \div ? = 153.85 \), we will follow these steps:

### Step 1: Approximate the squares
First, we approximate the squares of the numbers involved:
- \( 14.89 \approx 15 \) so \( 14.89^2 \approx 15^2 = 225 \)
- \( 11.16 \approx 11 \) so \( 11.16^2 \approx 11^2 = 121 \)

### Step 2: Substitute the approximated values
Now, substitute these approximated values into the equation:
\[ 225 - 121 + (299.92 + 350.15) \div ? = 153.85 \]

### Step 3: Calculate the difference
Calculate \( 225 - 121 \):
\[ 225 - 121 = 104 \]

### Step 4: Approximate the sum
Next, approximate the sum \( 299.92 + 350.15 \):
\[ 299.92 + 350.15 \approx 300 + 350 = 650 \]

### Step 5: Substitute back into the equation
Now substitute back into the equation:
\[ 104 + 650 \div ? = 153.85 \]

### Step 6: Isolate the division
Rearranging gives:
\[ 650 \div ? = 153.85 - 104 \]

### Step 7: Calculate the right side
Calculate \( 153.85 - 104 \):
\[ 153.85 - 104 \approx 49.85 \approx 50 \]

### Step 8: Set up the equation for the quotient
Now we have:
\[ 650 \div ? = 50 \]

### Step 9: Solve for ?
To find \( ? \), we rearrange:
\[ ? = \frac{650}{50} \]

### Step 10: Calculate the final value
Now, calculate:
\[ ? = 13 \]

Thus, the approximate value that will come in place of the question mark (?) is **13**.

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