A new temperature scale X is defined such that the freezing point of water is -20^ X and the boiling point of water is 130^ X . At what temperature on the Celsius scale will the reading on scale X be exactly double the reading on the Celsius scale?

Step-by-step solution

The relationship between the new scale X and the Celsius scale is given by equating the ratio of temperature differences: t_X - LFP _X UFP _X - LFP _X = t_C - LFP _C UFP _C - LFP _C Substituting the given fixed points for scale X ( -20^ X and 130^ X ) and the Celsius scale ( 0^ C and 100^ C ): t_X - (-20) 130 - (-20) = t_C - 0 100 - 0 t_X + 20 150 = t_C 100 t_X + 20 3 = t_C 2 We are given the condition that the reading on scale X is twice the reading on the Celsius scale, so t_X = 2t_C . Substituting this into the