Question 1132883
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This kind of system of equations comes up in a large number of very different kinds of problems: the sum of two numbers is x and their difference is y; what are the two numbers.<br>
Solving the problem using formal algebra is of course valid; and you should know how to set up and solve a problem like this using formal algebra.  But there is a quick path to the answer to this kind of problem using logical reasoning and simple mental arithmetic.<br>
Think of the operations of adding a second number to a first number, and subtracting that same second number from the first number, on a number line.<br>
You start at the first number; to add the second number you go one direction on the number line, and to subtract the second number you go the opposite direction.<br>
That means the first number is halfway between the two places you end up, which are the sum and difference of the two numbers.<br>
So the first number is just the average of the sum and difference of the two numbers; then the second number is the distance from the first number to either the sum or difference.<br>
For this example....<br>
sum = 70; difference = 18  -->  average is (70+18)/2 = 44<br>
So one of the numbers is 44; the other is 70-44 = 26, or 44-18 = 26.