Question 60613
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The sum of two numbers is 33. Their difference is 9. What are the two numbers? 
This is how I solved am I right if not what did I do wrong?
x+9=33
y-9=33
24+9=33
42-9=33
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        The answer by @consc198,  "Yes this is correct ",  is  WRONG.

        For a correct solution see what follows.



<pre>
Let the numbers be x and y: x the greater, y the smaller.


From the problem, you have these two equations

    x + y = 33,
    x - y =  9.


To find x, add the equations. You will get

    2x = 33 + 9,  or  2x = 42,  x = 42/2 = 21.


To find y, from the first equation subtract the second equation.  You will get

    y - (-y) = 33 - 9,  or  2y = 24,  y = 24/2 = 12.


<U>ANSWER</U>.  The numbers are 21 and 12.
</pre>

Solved correctly.



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For this problem, and for many other similar problems, there is a shortcut, 
which allows to get the answer MENTALLY and quickly:


- - - one number is half-the-sum, while the other number is half-the difference of the given numbers.


In our case, one number is  &nbsp;&nbsp;{{{(33+9)/2}}} = {{{42/2}}} = 21;  &nbsp;&nbsp;the other number is  &nbsp;&nbsp;{{{(33-9)/2}}} = {{{24/2}}} = 12.