The sum of 45% of a number and 20% of the same number of 4056. What is 85% of that number ?

Options

A. 5304
B. 5430
C. 5034
D. 5340

Answer

To solve the problem step by step, let's follow the instructions given in the question.

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Write the equation
According to the problem, the sum of 45% of the number and 20% of the same number equals 4056. We can express this mathematically as:
\[ 0.45x + 0.20x = 4056 \]

### Step 3: Combine like terms
Now, combine the terms on the left side of the equation:
\[ (0.45 + 0.20)x = 4056 \]
\[ 0.65x = 4056 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 0.65:
\[ x = \frac{4056}{0.65} \]
Calculating the right side:
\[ x = 6240 \]

### Step 5: Calculate 85% of \( x \)
Now that we have found \( x \), we need to calculate 85% of this number:
\[ 0.85x = 0.85 \times 6240 \]
Calculating this:
\[ 0.85 \times 6240 = 5304 \]

### Final Answer
Thus, 85% of the number is:
\[ \boxed{5304} \]

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