Browsing through Mr. Fox's old scientific notes, Bruce Wayne encounters a secret

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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 Batmobile'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.

Options:

A . 10℉

B . -4℉

C . 5℉

D . 0

Answer: Option B
:
B
Let's list what we know -

Browsing Through Mr. Fox's Old Scientific Notes, Bruce Wayne...

For any general scale with lower and upper fixed points labeled as T_L and T_u, and a measured temperature T, the ratio

will be the same, no matter what scale it is.
Extending that to ⁰Fand ⁰Z(in question), we have -

Browsing Through Mr. Fox's Old Scientific Notes, Bruce Wayne...

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