The sum of three numbers is 855. One of the numbers, x, is 50% more than the sum of the other two numbers. What is the value of x ?

Options

A. 570
B. 513
C. 214
D. 155

Answer

To solve the problem step by step, we will denote the three numbers as \( x \), \( y \), and \( z \).

### Step 1: Set up the equations
We know that the sum of the three numbers is 855. Therefore, we can write the equation:
\[ x + y + z = 855 \]

### Step 2: Express \( y + z \) in terms of \( x \)
From the equation above, we can express \( y + z \) as:
\[ y + z = 855 - x \]

### Step 3: Use the information about \( x \)
According to the problem, \( x \) is 50% more than the sum of the other two numbers \( y + z \). This can be expressed mathematically as:
\[ x = 1.5(y + z) \]

### Step 4: Substitute \( y + z \) into the equation for \( x \)
Now, we can substitute \( y + z \) from Step 2 into the equation from Step 3:
\[ x = 1.5(855 - x) \]

### Step 5: Solve for \( x \)
Now, we will distribute the 1.5:
\[ x = 1.5 \times 855 - 1.5x \]
\[ x + 1.5x = 1.5 \times 855 \]
\[ 2.5x = 1282.5 \]
Now, divide both sides by 2.5:
\[ x = \frac{1282.5}{2.5} = 513 \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{513} \]