SOLUTION: Two numbers is 18 and the difference is 6 what are the two numbers

Question 1104913: Two numbers is 18 and the difference is 6 what are the two numbers
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

"THE SUM OF two numbers is 18 and the difference is 6".

So x+y = 18 and x-y = 6.

Algebraically, we can add those two equations to find 2x = 24, so x = 12.
And then the other number must be 6.

Here is a way to analyze and solve the problem without using formal algebra.

Think of it this way:
You start with one number; when you add the second number you get 18 and when you subtract the second number you get 6.
The difference between those two results is 12; that difference is because you went one direction "on a number line" to get one result and the opposite direction to get the other result.
So that difference of 12 is twice the second number; that means the second number is 6.
And then using either of the given pieces of information you can find that the first number is 12.

While learning formal algebraic methods for solving problems is good mental exercise, it is equally valuable mental exercise to try to solve problems using logical reasoning.
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