SOLUTION: Two angles have a sum of 81 degrees. Their difference is 15 degrees. Find the angles

Question 1128974: Two angles have a sum of 81 degrees. Their difference is 15 degrees. Find the angles
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
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x + y = 81 x - y = 15 -------------------- Add these two equations. Answer. 48 and 33 degrees.

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

There are many types of problems that are basically the same as this: "The sum of two numbers is a; the difference is b; what are the two numbers?".

The other tutor has outlined the standard algebraic method for solving the problem; obviously that is a valid method.

However, since this kind of problem is encountered frequently, here is another way to get the answer by logical reasoning instead of formal algebra.

Think of it this way: you are starting with one number; when adding a second number you get 81 and when you subtract that same second number you get 15. That means the first number has to be exactly halfway between 81 and 15.

The number halfway between 81 and 15 is the average, (81+15)/2 = 96/2 = 48; then the second number is the difference between 48 and 15 (or between 48 and 81), which is 33.

If you look at the formal algebraic solution method, you are doing EXACTLY the same arithmetic; but if you can do this logical reasoning you will get to the answer faster and with less effort.

Here is another typical example of this kind of problem:

The sum of two numbers is 30, the difference is 6. Find the two numbers.

Solution:

The first number is the average of 30 and 6, which is 18.
The second number is the difference between 18 and 6, which is 12.
ANSWER: 18 and 12
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