What is the Correct Calculation for Jack's Homemade Temperature Scale?

[Betadine]

Homework Statement

Jack decides to create his own temperature scale. He places an uncalibrated mercury thermometer into an ice-water bath and records the mercury level as 20.0S. He then places the same thermometer above boiling water and records the mercury level as 170S. Finally, he divides the distance between these two levels into 150 equal lengths.

Calculate the reading on a Celsius thermometer when Jack's thermometer reads 95S.

Homework Equations

I used temperature, T = (x_T - x₀)/(x₁₀₀ - x₀) x 100.

The Attempt at a Solution

My answer is 50C. But the correct answer is 75C. Can anyone kindly help please?

 

[Bystander]

Is the problem statement exactly as you've transcribed it?

 

[Betadine]

By Bystander! Unfortunately, yes. Thanks for replying!

 

[Bystander]

Your equation (2. Relevant Eqtns.) is incomplete/ambiguous, but your answer is what I get. This has the "look" of problems that are re-cycled from year to year, or class to class, and frequently posted/assigned without proper proof-reading whenever the numbers are changed.