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"Vary depending on whether" is correct and usable in written English.
You can use it to refer to how two or more options are related to each other, usually in the context of making a decision. For example: "The cost of admission will vary depending on whether you purchase a single-day pass or a multi-day pass."
Exact(60)
Attaching the strap will vary, depending on whether or not you've got one or two strap pegs.
Workouts vary, depending on whether you want a leaner body or a stronger one, for example.
Ticket prices vary depending on whether you want to hit up all three cities or just visit one or two.
Disability benefits for veterans can vary depending on whether an injury is considered psychological or physical.
Prices in Mattituck vary, depending on whether the property is inland or on the water.
But these amounts can vary depending on whether investors choose to reinvest their dividends.
These factors can all vary depending on whether the firm is small, medium or large.
Housing costs will vary depending on whether you choose to live on or off-campus.
Stamp duty and transfer taxes vary depending on whether a property is new or being resold.
And within matte surfaces visual textures subtly vary depending on whether color has been drawn, brushed, washed or dabbed on.
Symptoms also tended to vary depending on whether the pot was consumed as an edible or smoked.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com