The total mass of a box and 3 similar tennis balls is 1.02 kg. When the number of tennis balls in the box is tripled, the total mass becomes 2.16 kg. Find the mass of the empty box. Give your answer in kilograms.
Let the mass of the box be $x$ and the mass of a tennis ball be $y$. Then, we can set up the following system of equations:
\begin{align*}
x + 3y &= 1.02 \\
x + 9y &= 2.16 \\
\end{align*}
Subtracting the first equation from the second equation, we have $6y = 1.14$. Dividing by 6, we get $y = 0.19$. Plugging this value into the first equation, we have $x + 3(0.19) = 1.02$, so $x + 0.57 = 1.02$. Subtracting 0.57 from both sides gives $x = \boxed{0.45}$ kilograms.