What is the common usage for "let" for multiple variables?

Question

Should I use

Let $x$ be (...), let $y$ be (...), ...

or

Let $x$ be (...). Let $y$ be (...). ...

or

Let $x$ be (...), $y$ be (...), ...

or even something different? What variant is commonly used in English?

Answer 1

All three are common. The second variant is preferred if the descriptions are long.