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Tom is thinking of two numbers? OK, we'll call them A and B.

We know the sum (adding) is 22.

So, A + B = 22.

The difference (subtracting) is 12, so

A - B = 12

Let's use substitution to help us.

Solve one equation for a variable, A or B. It doesn't matter.

A + B = 22

A = 22 - B

So A = 22 - B. We can plug this value of A into our other equation to figure out what B is.

A - B = 12 (remember to use parenthesis when you substitute)

(22 - B) - B = 12

And simplify.

22 -2B = 12

2(11-B) = 12

11-B = 6

-B = -5

B = 5.

Now that we found B, substitute it into either equation to find A.

however, we have an equation that tells us what A is.

A = 22 - B

A = 22 - 5

A = 17.

To check, plug A = 17 and B = 5 into both equations and see if it works.

A + B = 22

17 + 5 = 22

22 = 22 (check)

A - B = 12

17 - 5 = 12

12 = 12 (check)

Q: If tom is thinking of two numbers their sum is 22 and the difference is 12 what are the numbers?

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