Question
A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18. Find the two integers.
A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/18. Find the two integers.
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Koala Tutor
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Let the two positive integers be $x$ and $2x$. We are given that $$\frac{1}{x} - \frac{1}{2x} = \frac{1}{18}.$$Multiplying both sides by $18x$ gives $$18 - 9 = x.$$Therefore, we have $x = 9$. The two positive integers are $\boxed{9}$ and $\boxed{18}$.
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