If the sum of x and 20 is 8 more than the distance of 10 and y, what is the value of `x + y` ?

Options

A. `-2`
B. `8`
C. `9`
D. 28

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem statement
We need to translate the given statement into a mathematical equation. The statement says: "If the sum of x and 20 is 8 more than the distance of 10 and y."

### Step 2: Write the mathematical expression
The sum of x and 20 can be expressed as:
\[ x + 20 \]

The distance between 10 and y can be expressed as:
\[ |10 - y| \]

According to the problem, we can set up the equation:
\[ x + 20 = |10 - y| + 8 \]

### Step 3: Simplify the equation
Since we are not given specific conditions for y, we will consider the absolute value definition. We can break it into two cases based on the value of y.

**Case 1:** \( y \leq 10 \)
In this case, \( |10 - y| = 10 - y \). The equation becomes:
\[ x + 20 = (10 - y) + 8 \]
\[ x + 20 = 18 - y \]

**Case 2:** \( y > 10 \)
In this case, \( |10 - y| = y - 10 \). The equation becomes:
\[ x + 20 = (y - 10) + 8 \]
\[ x + 20 = y - 2 \]

### Step 4: Solve for x + y in both cases

**For Case 1:**
From \( x + 20 = 18 - y \):
Rearranging gives:
\[ x + y = 18 - 20 \]
\[ x + y = -2 \]

**For Case 2:**
From \( x + 20 = y - 2 \):
Rearranging gives:
\[ x + y = -2 + 20 \]
\[ x + y = 18 \]

### Step 5: Conclusion
Since both cases yield a different result, we need to check the conditions.

1. For \( y \leq 10 \), we found \( x + y = -2 \).
2. For \( y > 10 \), we found \( x + y = 18 \).

However, since the problem does not specify any restrictions on y, we can conclude that the value of \( x + y \) can be either -2 or 18 depending on the value of y.

### Final Answer
The value of \( x + y \) can be -2 or 18.