Find the approximate value of (?) in the following questions.
`? xx 24.023 + (1)/(2)"of 419.991" = (3)/(4) "of 984.034"`

Options

A. 8
B. 10
C. 22
D. 14

Answer

To solve the equation and find the approximate value of the question mark (?), we will follow these steps:

### Step 1: Write the equation
The equation given is:
\[ ? \times 24.023 + \frac{1}{2} \times 419.991 = \frac{3}{4} \times 984.034 \]

### Step 2: Approximate the values
For simplification, we can round the numbers to the nearest whole numbers:
- \( 24.023 \approx 24 \)
- \( 419.991 \approx 420 \)
- \( 984.034 \approx 984 \)

So, the equation becomes:
\[ ? \times 24 + \frac{1}{2} \times 420 = \frac{3}{4} \times 984 \]

### Step 3: Calculate \(\frac{1}{2} \times 420\)
Calculating \(\frac{1}{2} \times 420\):
\[ \frac{1}{2} \times 420 = 210 \]

### Step 4: Calculate \(\frac{3}{4} \times 984\)
Calculating \(\frac{3}{4} \times 984\):
\[ \frac{3}{4} \times 984 = 738 \]

### Step 5: Substitute back into the equation
Now substitute these values back into the equation:
\[ ? \times 24 + 210 = 738 \]

### Step 6: Isolate the question mark
To isolate ?, subtract 210 from both sides:
\[ ? \times 24 = 738 - 210 \]
\[ ? \times 24 = 528 \]

### Step 7: Solve for ?
Now, divide both sides by 24:
\[ ? = \frac{528}{24} \]

### Step 8: Calculate the final value
Calculating \(\frac{528}{24}\):
\[ ? = 22 \]

Thus, the approximate value of ? is **22**.