89% of ? + 365 = 1075.22

Options

A. 798
B. 897
C. 898
D. 752

Answer

To solve the equation \( 89\% \text{ of } ? + 365 = 1075.22 \), we can follow these steps:

### Step 1: Convert the percentage to a decimal
First, we need to express \( 89\% \) as a decimal. This is done by dividing \( 89 \) by \( 100 \):
\[ 89\% = \frac{89}{100} \]

### Step 2: Set up the equation
Let \( x \) represent the question mark. The equation can be rewritten as:
\[ \frac{89}{100} \cdot x + 365 = 1075.22 \]

### Step 3: Isolate the term with \( x \)
To isolate the term with \( x \), we need to subtract \( 365 \) from both sides of the equation:
\[ \frac{89}{100} \cdot x = 1075.22 - 365 \]

### Step 4: Calculate the right side
Now, we perform the subtraction:
\[ 1075.22 - 365 = 710.22 \]
So, we have:
\[ \frac{89}{100} \cdot x = 710.22 \]

### Step 5: Solve for \( x \)
To solve for \( x \), we can multiply both sides by \( \frac{100}{89} \):
\[ x = 710.22 \cdot \frac{100}{89} \]

### Step 6: Calculate the value of \( x \)
Now, we compute the value:
\[ x = \frac{71022}{89} \approx 798 \]

### Final Answer
Thus, the value of \( x \) (the question mark) is:
\[ x \approx 798 \]

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