As part of their end of semester project, students in a science class are asked to devise a temperature scale. The diagram below shows the work of two of the students Paul and Simon. P₁ = +12.0°P and P₂ = +110°P correspond to the melting point of ice and boiling point of water respectively on the Paul scale, while S₁ = -9.00°S and S₂ = +80.0°S correspond to the melting point of ice and boiling point of water on the Simon scale. Assume that each division represents a degree on both scales.

(a) How many degrees on the Simon scale correspond to 1°P on the Paul scale? 1°P =  °S 

(b) If a particular temperature measurement reads +50.0°P on the Paul scale, what would this same temperature measurement read on the Simon scale? T_S =  °S