What approximate value should come in place of the question mark (?) in the following equation? `29 cdot 98 xx 37 cdot 05 div ? + 7 cdot 45 = 100cdot 5`

Options

A. 10
B. 13
C. `14.cdot 5`
D. 12

Answer

To solve the equation \( 29.98 \times 37.05 \div ? + 7.45 = 100.5 \), we will follow these steps:

### Step 1: Isolate the term with the question mark
We start by isolating the term that contains the question mark. We can do this by subtracting \( 7.45 \) from both sides of the equation.

\[ 29.98 \times 37.05 \div ? = 100.5 - 7.45 \]

### Step 2: Calculate the right side of the equation
Now, we will perform the subtraction on the right side:

\[ 100.5 - 7.45 = 93.05 \]

So now we have:

\[ 29.98 \times 37.05 \div ? = 93.05 \]

### Step 3: Multiply both sides by the question mark
Next, we multiply both sides of the equation by the question mark to eliminate the division:

\[ 29.98 \times 37.05 = 93.05 \times ? \]

### Step 4: Calculate \( 29.98 \times 37.05 \)
Now, we need to calculate \( 29.98 \times 37.05 \). For approximation, we can round \( 29.98 \) to \( 30 \) and \( 37.05 \) to \( 37 \):

\[ 30 \times 37 = 1110 \]

### Step 5: Substitute back into the equation
Now we substitute back into the equation:

\[ 1110 = 93.05 \times ? \]

### Step 6: Solve for the question mark
To find the value of the question mark, we divide both sides by \( 93.05 \):

\[ ? = \frac{1110}{93.05} \]

### Step 7: Calculate the division
Now we perform the division:

\[ ? \approx 11.91 \]

### Step 8: Round to the nearest option
The approximate value of \( ? \) is \( 11.91 \). The closest option from the given choices (10, 13, 14.5, 12) is \( 12 \).

Thus, the approximate value that should come in place of the question mark is:

\[ \boxed{12} \]

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