On a new Jekyll temperature scale, water freezes at 17 degrees J and boils

On a new Jekyll temperature scale, water freezes at 17 degrees J and boils at 97 degrees J.  On another new temperature scale, the Hyde scale, water freezes at 0 degrees H and boils at 120 degrees H.  If methyl alcohol boils at 84 degrees H, what is its boiling point on the Jekyll scale?

Upon initially reading this problem, I thought that it would be necessary to set both freezing and boiling points for both scales equal to each other to obtain a ratio.  However, after further consideration, it was much more simple then that.

Since the question was specifically asking about the boiling points, I realized that by setting the equation equal to Jekyll’s, the answer could be easily calculated.  The first step was to find the difference in boiling points between Jekyll’s and Hyde’s (97 degrees J – 120 degrees H = 23).  After figuring out the difference I was able to set up my equation for to solve for Jekyll’s as (J = H – 23).  Since I was given the boiling point for Hide’s for methyl alcohol of 84, I plugged that in for the “H” in the equation.  This in turn gave me my answer of 61 degrees as the boiling point for methyl alcohol in Jekyll’s.