Sum of Two Positive Integers

N and Y are positive integers, N\neq Y. If N\times Y\div 2=N+Y, what is the sum N+Y?
Source: NCTM Mathematics Teacher 2008

SOLUTION
N\times Y\div 2=N+Y
NY=2(N+Y)
NY-2Y=2N
Y(N-2)=2N
Y=\dfrac{2N}{N-2}
Table of N and Y values
N\qquad Y
1\qquad -2
2\qquad\text{undefined}
3\qquad 6
4\qquad 4
5\qquad 3.33
6\qquad 3
7\qquad 2.8
8\qquad 2.67
9\qquad 2.57
10\qquad 2.5
\cdots
The graph of Y as a function of N shows a horizontal asymptote at Y=2. For N>6,\: 2<Y<3.

Two possible values of (N,Y):(3,6) or (6,3).
N+Y=3+6=9

Answer: 9

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About mvtrinh

Retired high school math teacher.
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