In each of the following questions, find the exact value of (?)
15% of 250 + 35% of 750 - 75 = `(?)^(2)`

Options

A. 15
B. 16
C. 18
D. 10

Answer

To solve the equation \( 15\% \text{ of } 250 + 35\% \text{ of } 750 - 75 = (?)^2 \), we will follow these steps:

### Step 1: Calculate 15% of 250
To find 15% of 250, we can use the formula:
\[ \text{Percentage} = \frac{\text{Percent}}{100} \times \text{Total} \]
So,
\[ 15\% \text{ of } 250 = \frac{15}{100} \times 250 = 0.15 \times 250 = 37.5 \]

### Step 2: Calculate 35% of 750
Next, we calculate 35% of 750 using the same formula:
\[ 35\% \text{ of } 750 = \frac{35}{100} \times 750 = 0.35 \times 750 = 262.5 \]

### Step 3: Combine the results and subtract 75
Now, we add the results from Step 1 and Step 2, and then subtract 75:
\[ 37.5 + 262.5 - 75 \]
Calculating this step by step:
\[ 37.5 + 262.5 = 300 \]
Then,
\[ 300 - 75 = 225 \]

### Step 4: Set the equation to find (?)
Now we have:
\[ 225 = (?)^2 \]

### Step 5: Solve for (?)
To find \( ? \), we take the square root of both sides:
\[ ? = \sqrt{225} = 15 \]

Thus, the exact value of \( ? \) is **15**.