Question 1104913
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"THE SUM OF two numbers is 18 and the difference is 6".<br>
So x+y = 18 and x-y = 6.<br>
Algebraically, we can add those two equations to find 2x = 24, so x = 12.
And then the other number must be 6.<br>
Here is a way to analyze and solve the problem without using formal algebra.<br>
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.<br>
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.