`?% "of" 658 + 40% "of" 845=568.3`

Options

A. 46
B. 42
C. 38
D. 35

Explanation

To solve the equation \( ?\% \text{ of } 658 + 40\% \text{ of } 845 = 568.3 \), we will follow these steps:

### Step 1: Convert percentages to decimal form
Let \( x \) be the unknown percentage. Therefore, \( ?\% \) can be written as \( \frac{x}{100} \).

### Step 2: Write the equation
The equation can be rewritten as:
\[ \frac{x}{100} \times 658 + \frac{40}{100} \times 845 = 568.3 \]

### Step 3: Simplify the equation
Calculate \( 40\% \text{ of } 845 \):
\[ \frac{40}{100} \times 845 = 0.4 \times 845 = 338 \]
Now substitute this back into the equation:
\[ \frac{x}{100} \times 658 + 338 = 568.3 \]

### Step 4: Isolate the term with \( x \)
Subtract 338 from both sides:
\[ \frac{x}{100} \times 658 = 568.3 - 338 \]
Calculating the right side:
\[ 568.3 - 338 = 230.3 \]
So now we have:
\[ \frac{x}{100} \times 658 = 230.3 \]

### Step 5: Solve for \( x \)
Multiply both sides by 100 to eliminate the fraction:
\[ x \times 658 = 23030 \]
Now, divide both sides by 658:
\[ x = \frac{23030}{658} \]

### Step 6: Calculate the value of \( x \)
Calculating the division:
\[ x \approx 35 \]

Thus, the required percentage \( ? \) is \( 35\% \).

### Summary of Steps:
1. Convert the unknown percentage to decimal form.
2. Rewrite the equation with the known values.
3. Simplify the equation by calculating \( 40\% \text{ of } 845 \).
4. Isolate the term with \( x \).
5. Solve for \( x \) by multiplying and dividing appropriately.
6. Calculate the final value.