SOLUTION: Two numbers total 61 and have a difference of 13. Find the two numbers.

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Question 1108753: Two numbers total 61 and have a difference of 13. Find the two numbers.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
x + y = 61
x - y = 13
-------------------Add the two equations and see what will happen . . .


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The algebraic solution outlined by the other tutor is certainly valid; you should know how to solve problems like this using that method.

But it is also good to be able to understand what is happening in the problem so you can see how to get the solution informally, by logical reasoning.

For this type of problem, where you are given the sum and difference of two numbers, think of a number line. You start at one of the two numbers; to get the sum of the two numbers, you go one direction on the number line from the first number; to get the difference, you go the opposite direction.

That means the first number is halfway between the sum and difference of the two numbers -- i.e., it is the average of the sum and difference.

So in this example, a quick way to the solution is to see one number as %2861%2B13%29%2F2+=+74%2F2+=+37; then the other number must be 24.