If \(x+y=70\) and \(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{84}\), what is \(xy\) if the variables are positive integers?
1/x + 1/y = (x + y) / xy = 70/ xy
So
70 / xy = 5/84 cross-multiply
84 * 70 = 5 xy
84 * 70 / 5 xy
84 * 14 = xy
But we need to have x + y = 70
Note that if we divide 84 by 2 and multiply 14 by 2 we have
42 * 28 = xy
And x + y = 70