Sum of their Reciprocal is also Given

Algebra Level 2

If x + y = 70 x+y=70 and 1 x + 1 y = 5 84 \dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{84} , what is x y xy if the variables are positive integers?


The answer is 1176.

Kaizen Cyrus by Kaizen Cyrus , 18, Philippines

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1 solution

Joshua Lowrance
Feb 13, 2019

1 x + 1 y = 5 84 \frac{1}{x}+\frac{1}{y}=\frac{5}{84}

x + y x y = 5 84 \frac{x+y}{xy}=\frac{5}{84}

70 x y = 5 84 \frac{70}{xy}=\frac{5}{84}

70 × 84 5 = x y \frac{70\times 84}{5}=xy

1176 = x y 1176=xy

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