45% of?- 48% of 1105 = 911. 40

Options

A. 3204
B. 3402
C. 3604
D. 3406

Answer

To solve the equation \( 45\% \text{ of } ? - 48\% \text{ of } 1105 = 911.40 \), we can follow these steps:

### Step 1: Convert percentages to fractions
We know that:
- \( 45\% = \frac{45}{100} \)
- \( 48\% = \frac{48}{100} \)

So we can rewrite the equation as:
\[ \frac{45}{100} \cdot x - \frac{48}{100} \cdot 1105 = 911.40 \]

### Step 2: Calculate \( 48\% \text{ of } 1105 \)
Now, let's calculate \( \frac{48}{100} \cdot 1105 \):
\[ \frac{48 \cdot 1105}{100} = \frac{52920}{100} = 529.20 \]

### Step 3: Substitute back into the equation
Substituting this value back into the equation gives us:
\[ \frac{45}{100} \cdot x - 529.20 = 911.40 \]

### Step 4: Isolate \( \frac{45}{100} \cdot x \)
Now, we can isolate \( \frac{45}{100} \cdot x \) by adding \( 529.20 \) to both sides:
\[ \frac{45}{100} \cdot x = 911.40 + 529.20 \]
\[ \frac{45}{100} \cdot x = 1440.60 \]

### Step 5: Solve for \( x \)
Next, to find \( x \), we multiply both sides by the reciprocal of \( \frac{45}{100} \), which is \( \frac{100}{45} \):
\[ x = 1440.60 \cdot \frac{100}{45} \]

### Step 6: Calculate \( x \)
Now, we calculate:
\[ x = \frac{144060}{45} = 3200 \]

### Final Answer
Thus, the value of \( ? \) is \( 3200 \).

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