Find two numbers such that one of the numbers is 8 more than the other and their sum is 54.

Answer

To solve the problem of finding two numbers where one number is 8 more than the other and their sum is 54, we can follow these steps:

### Step 1: Define the Variables
Let the first number be \( x \). Since the second number is 8 more than the first number, we can express the second number as \( x + 8 \).

### Step 2: Set Up the Equation
According to the problem, the sum of the two numbers is 54. Therefore, we can write the equation:
\[ x + (x + 8) = 54 \]

### Step 3: Simplify the Equation
Now, simplify the left side of the equation:
\[ x + x + 8 = 54 \]
This simplifies to:
\[ 2x + 8 = 54 \]

### Step 4: Isolate the Variable
Next, we need to isolate \( 2x \). To do this, subtract 8 from both sides:
\[ 2x + 8 - 8 = 54 - 8 \]
This simplifies to:
\[ 2x = 46 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{46}{2} \]
This gives us:
\[ x = 23 \]

### Step 6: Find the Second Number
Now that we have the first number, we can find the second number by substituting \( x \) back into the expression for the second number:
\[ \text{Second number} = x + 8 = 23 + 8 = 31 \]

### Conclusion
The two numbers are 23 and 31.