Answer
The number is $1$ and its reciprocal is $1$ or the number is $2$ and its reciprocal is $\dfrac{1}{2}.$
Work Step by Step
Let $x$ be the number.
The conditions of the problem translate to
\begin{array}{l}\require{cancel}
x+2\left(\dfrac{1}{x}\right)=3
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x+\dfrac{2}{x}=3
\\\\
x\left( x+\dfrac{2}{x} \right)=(3)x
\\\\
x^2+2=3x
\\\\
x^2-3x+2=0
\\\\
(x-2)(x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Property) and then solving for the variable, then $
x=\{ 1,2 \}
.$
Hence, the number is $1$ and its reciprocal is $1$ or the number is $2$ and its reciprocal is $\dfrac{1}{2}.$
