SOLUTION: The sum of two numbers is 89. Their difference is 23. What are the two numbers?

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Question 1185069: The sum of two numbers is 89. Their difference is 23. What are the two numbers?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
...two numbers...
 Let x = the larger
 Let y = the smaller

The sum of two numbers is 89.
 x + y = 89

Their difference is 23.
 
 x - y = 23

What are the two numbers?
Write the two equations one under the other
and add them term by term:

 x + y =  89
 x - y =  23
------------
2x     = 112

Divide both sides by 2:

     x = 56

Substitute in

 x + y = 89
56 + y = 89
     y = 33

The larger number is 56 and the smaller is 33.

Check:  Add them 56+33 = 89.  That checks.
        Subtract them: 56-33 = 23. That checks.  Woo hoo!

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


This kind of calculation comes up in a wide variety of math problems: b added to a gives one number; b subtracted from a gives a second number.

Unless a formal algebraic solution is required, you can solve this kind of problem quickly with a bit of mental arithmetic.

The given sum and difference are 89 and 23.
The difference between 89 and 23 is 66.
Half of 66 is 33.
The second number is 33; the first is 23+33=56 (or 89-33=56).

ANSWERS: 56 and 33

The reasoning for that simple solution is that 89 is the second number MORE THAN the first and 23 is the second number LESS THAN the first -- so the difference between 89 and 23 is twice the second number.
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