Find a linear equation to solve for the following unknown quantities: One number exceeds another number by 23 and their sum is 33. Find the two numbers.

(Seperate answers with a comma.)

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

We are given two conditions:

1. One number exceeds the other by 23, which can be expressed as:
   \[
   x = y + 23
   \]
2. The sum of the two numbers is 33, so:
   \[
   x + y = 33
   \]

Now, substitute \( x = y + 23 \) into the second equation:

\[
(y + 23) + y = 33
\]

Simplify and solve for \( y \):

\[
2y + 23 = 33
\]

Subtract 23 from both sides:

\[
2y = 10
\]

Now, divide by 2:

\[
y = 5
\]

Now that we know \( y = 5 \), substitute it back into the first equation to find \( x \):

\[
x = 5 + 23 = 28
\]

Thus, the two numbers are:
\[
\boxed{28, 5}
\]

Would you like further details or have any questions? Here are five related questions for practice:

1. What would the numbers be if one exceeded the other by 15 and their sum was 45?
2. How would you solve if the difference between the numbers was 18 and their sum was 50?
3. If the sum was 60 and the larger number was twice the smaller, what would the numbers be?
4. What are the two numbers if their difference is 7 and their sum is 31?
5. If one number exceeds another by 12 and their sum is 40, what are the two numbers?

**Tip:** When solving word problems involving numbers, it's helpful to clearly define variables and set up equations that reflect the given relationships.

Find a linear equation to solve for the following unknown quantities: One number exceeds another number by 23 and their sum is 33. Find the two numbers.

Learn how to solve a linear equation where one number exceeds another by 23 and their sum is 33. This step-by-step solution involves key algebraic concepts and simple linear equations, suitable for students in Grades 6-8.

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