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The problem states:

- The sum of two numbers is 90.
- Their difference is 12.
- We are asked to find the two numbers.

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

We have the following system of equations:

1. \( x + y = 90 \) (the sum of the two numbers)
2. \( x - y = 12 \) (the difference of the two numbers)

Now, we can solve this system of equations using the addition method. By adding both equations:

\[
(x + y) + (x - y) = 90 + 12
\]

Simplifying:

\[
2x = 102
\]

Solving for \( x \):

\[
x = \frac{102}{2} = 51
\]

Now substitute \( x = 51 \) into the first equation \( x + y = 90 \):

\[
51 + y = 90
\]

Solving for \( y \):

\[
y = 90 - 51 = 39
\]

Thus, the two numbers are \( 51 \) and \( 39 \).

Would you like further details on how I solved this? Or do you have another question?

Here are some related questions you can explore:
1. How do you solve systems of linear equations by substitution?
2. What are some real-world applications of systems of equations?
3. How do you graph the solutions to a system of linear equations?
4. How can we solve a system of equations if one equation involves multiplication?
5. How do you check the solution to a system of equations?

Tip: When solving systems of equations, always check your solutions by substituting them back into the original equations to verify they satisfy both equations.

The sum of two numbers is 90. The difference is 12. What are the numbers?

Learn how to solve a system of linear equations where the sum of two numbers is 90 and their difference is 12. This problem covers key algebraic methods like addition and substitution, suitable for students in Grades 6-8.

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