`50% "of" ?=30% "of" 600+25% "of" 160`

Options

A. 440
B. 400
C. 380
D. 200

Explanation

To solve the equation \(50\% \text{ of } ? = 30\% \text{ of } 600 + 25\% \text{ of } 160\), we will follow these steps:

### Step 1: Set up the equation
Let \(x\) represent the unknown value (the question mark). The equation can be set up as:
\[ 50\% \text{ of } x = 30\% \text{ of } 600 + 25\% \text{ of } 160 \]

### Step 2: Convert percentages to decimal form
Convert the percentages to decimals:
- \(50\% = \frac{50}{100} = 0.5\)
- \(30\% = \frac{30}{100} = 0.3\)
- \(25\% = \frac{25}{100} = 0.25\)

### Step 3: Rewrite the equation using decimals
Now, rewrite the equation:
\[ 0.5x = 0.3 \times 600 + 0.25 \times 160 \]

### Step 4: Calculate the right side of the equation
Calculate \(30\% \text{ of } 600\) and \(25\% \text{ of } 160\):
- \(0.3 \times 600 = 180\)
- \(0.25 \times 160 = 40\)

Now substitute these values back into the equation:
\[ 0.5x = 180 + 40 \]

### Step 5: Simplify the right side
Add the two results:
\[ 0.5x = 220 \]

### Step 6: Solve for \(x\)
To find \(x\), divide both sides by \(0.5\):
\[ x = \frac{220}{0.5} \]
This is equivalent to multiplying by 2:
\[ x = 220 \times 2 = 440 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{440} \]