Browsing through Mr. Fox's old scientific notes, Bruce Wayne encounters a secret temperature scale, which Mr. Fox called Z, in order to keep the Bat mobile's technology a secret. On that scale, the freezing and the boiling points of water were recorded to be -70Z and 780Z, respectively. The records instruct to maintain the coolant temperature at -240Z for top speed. Mr. Wayne, naturally comfortable with the Fahrenheit scale due to his American upbringing, needs to calculate the coolant temperature in 0F. Help him choose the correct value
Let's list what we know -
For any general scale with lower and upper fixed points labeled as TL and Tu, and a measured temperature T,, the ratio will be the same, no matter what scale it is.
Extending that to 0F and 0Z (in question), we have -