Two numbers have a sum of 18. Find the numbers if one number is 8 larger than the other. Solve it algebraically.

Let the two numbers be \( x \) and \( y \).

From the problem, we have the following two conditions:

1. The sum of the two numbers is 18:
   \[
   x + y = 18
   \]

2. One number is 8 larger than the other:
   \[
   x = y + 8
   \]

Now, substitute the second equation into the first:

\[
(y + 8) + y = 18
\]

Simplify the equation:

\[
2y + 8 = 18
\]

Subtract 8 from both sides:

\[
2y = 10
\]

Divide both sides by 2:

\[
y = 5
\]

Now, substitute \( y = 5 \) into the equation \( x = y + 8 \):

\[
x = 5 + 8 = 13
\]

Thus, the two numbers are \( 13 \) and \( 5 \).

### Final Answer:
The two numbers are \( 13 \) and \( 5 \).

Would you like a detailed breakdown or have any questions? Here are some related questions to practice:

1. If two numbers have a sum of 24 and one is 10 larger than the other, what are the numbers?
2. Solve algebraically: The sum of two numbers is 30, and one is 4 times the other.
3. The sum of two numbers is 50, and one is twice the other. Find the numbers.
4. If two numbers have a sum of 40 and one is 12 larger than the other, what are the numbers?
5. Solve: The sum of two numbers is 35, and one number is 5 more than twice the other.

**Tip**: When working with two variables, substitute one equation into the other to reduce the system to a single variable.

Learn how to solve the algebraic problem where two numbers have a sum of 18, and one number is 8 larger than the other. Follow a step-by-step explanation using basic algebra and the substitution method. Suitable for students in Grades 6-8.

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