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OSCOLPHYS$201613\mathrm{.}1.$WA$\mathrm{.}004.$TUTORIAL.

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. $P_1=+16\mathrm{.}0P$ and $P_2=+125P$ correspond to the melting point of ice and boiling point of water respectively on the Paul scale, while $S_1=-5\mathrm{.}00S$ and $S_2=+70\mathrm{.}0S$ 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 $1P$ on the Paul scale?

$1P=s$

$($b$)$ If a particular temperature measurement reads $+50\mathrm{.}0P$ on the Paul scale, what would this same temperature measurement read on the Simon scale?

$T_S=S$