SOLUTION: Find two numbers whose sum is 70 and whose difference is 18.

Algebra.Com
Question 1132883: Find two numbers whose sum is
70 and whose difference is
18.
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
x + y = 70

x - y = 18.

---------------------  Add the equations and see what will happen.


ANSWER.  x =  = 44;   y =  = 26.

Solved, answered, explained and completed.


Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

Easily solvable using Elimination Method
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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.

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.

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.

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.

That means the first number is halfway between the two places you end up, which are the sum and difference of the two numbers.

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.

For this example....

sum = 70; difference = 18 --> average is (70+18)/2 = 44

So one of the numbers is 44; the other is 70-44 = 26, or 44-18 = 26.
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