13% of `258-? = 10`

Options

A. 23.45
B. 24.53
C. 23.54
D. 24.35

Explanation

To solve the equation \( 13\% \text{ of } (258 - ?) = 10 \), we will follow these steps:

### Step 1: Convert the percentage to a decimal
First, we need to express 13% as a decimal.
\[ 13\% = \frac{13}{100} = 0.13 \]

### Step 2: Set up the equation
Now we can rewrite the equation using the decimal form:
\[ 0.13 \times (258 - x) = 10 \]

### Step 3: Distribute the 0.13
Next, we will distribute \(0.13\) across the expression \( (258 - x) \):
\[ 0.13 \times 258 - 0.13x = 10 \]

### Step 4: Calculate \(0.13 \times 258\)
Now we will calculate \(0.13 \times 258\):
\[ 0.13 \times 258 = 33.54 \]
So the equation simplifies to:
\[ 33.54 - 0.13x = 10 \]

### Step 5: Isolate the variable \(x\)
Next, we will isolate \(x\) by moving \(33.54\) to the other side of the equation:
\[ -0.13x = 10 - 33.54 \]
Calculating the right side gives:
\[ -0.13x = -23.54 \]

### Step 6: Solve for \(x\)
Now, we will divide both sides by \(-0.13\) to solve for \(x\):
\[ x = \frac{-23.54}{-0.13} \]
Calculating this gives:
\[ x = 181.08 \]

### Final Answer
Thus, the value of \(x\) (or the question mark) is:
\[ x = 181.08 \]