The difference between 55% of a number and 14% of the same number is 8610. What is 85% of that number ?

Options

A. 17850
B. 16820
C. 18020
D. 19450

Answer

To solve the problem step by step, we need to find the number based on the given information and then calculate 85% of that number.

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

### Step 2: Set up the equation
According to the problem, the difference between 55% of the number and 14% of the number is 8610. We can express this mathematically as:
\[ 0.55x - 0.14x = 8610 \]

### Step 3: Simplify the equation
Combine the percentages:
\[ (0.55 - 0.14)x = 8610 \]
\[ 0.41x = 8610 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 0.41:
\[ x = \frac{8610}{0.41} \]
Calculating this gives:
\[ x = 21000 \]

### Step 5: Calculate 85% of \( x \)
Now that we have the value of \( x \), we need to find 85% of it:
\[ 0.85x = 0.85 \times 21000 \]
Calculating this gives:
\[ 0.85 \times 21000 = 17850 \]

### Final Answer
Thus, 85% of the number is:
\[ \boxed{17850} \]

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