Question 478004
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The sum of two numbers is 248. Their difference is 64. find the number.
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        The solution to this problem in the post by @Theo,  giving the answer   x = 164,  y = 100,   is incorrect.  

        It does not satisfy the condition   x+y = 248.


        I came to bring a correct solution.



<pre>
Let x be the greater number, y be the smaller number.


We have then these two equations

    x + y = 248,    (1)

    x - y =  64.    (2)


You can solve this system of two linear equations by the Substitution method
or by the Elimination method, on your choice.


Let' solve by the Elimination method.


Add equations (1) and (2).  The terms with 'y' will annihilate,
and you will get

    2x = 248 + 64 = 312,

     x            = 312/2 = 156.


Now find 'y' from equation (1)

    y = 248 - x = 248 - 156 = 184.


<U>ANSWER</U>.  x = 156, y = 92.


<U>CHECK</U>.  x + y = 156 + 92 = 248  (correct).  x - y = 156 - 92 = 64  (correct).
</pre>

Solved correctly.