Linear relations practice worksheet with algebraic problems and exercises.

Problem Statement:

The average of two numbers is 13. If one of the numbers is 8, find the other number.

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Solution:

#### Step 1: Understand the problem
We are given:
- The average of two numbers is 13.
- One of the numbers is 8.
- We need to find the other number.

#### Step 2: Recall the formula for the average of two numbers
The average of two numbers \( a \) and \( b \) is given by:
\[
\text{Average} = \frac{a + b}{2}
\]

#### Step 3: Set up the equation
Let the two numbers be \( x \) and \( y \). We are given:
- One of the numbers, say \( x = 8 \).
- The average of the two numbers is 13.

Using the average formula:
\[
\frac{x + y}{2} = 13
\]

Substitute \( x = 8 \) into the equation:
\[
\frac{8 + y}{2} = 13
\]

#### Step 4: Solve for \( y \)
To isolate \( y \), first eliminate the fraction by multiplying both sides of the equation by 2:
\[
8 + y = 26
\]

Next, solve for \( y \) by subtracting 8 from both sides:
\[
y = 26 - 8
\]
\[
y = 18
\]

#### Step 5: Verify the solution
To ensure the solution is correct, calculate the average of the two numbers \( x = 8 \) and \( y = 18 \):
\[
\text{Average} = \frac{8 + 18}{2} = \frac{26}{2} = 13
\]
The average is indeed 13, so the solution is verified.

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Final Answer:

\[
\boxed{18}
\]