Question 1165018: Tom Jones and Bill Smith set out to create their own thermometers. Jones calls the freezing point of
8' water on his scale 40 degrees, while Smith calls his freezing point 25 degrees. Jones makes the boiling
L{ 6 TC point of water 280 degrees, and Smith, 125 degrees. What temperature on the Smith scale is equivalent
'1 8x6 to 97 degrees on the Jones scale (to 1/10 of a degree)?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm assuming you are comparing their freezing point and their boiling points with comparable units.
if not, then this answer is not good.
the method is the same as used to convert from fahrenheit to centigrade and vice versa.
you have:
smith = 25 degrees freezing point and 125 degrees boiling point.
jones = 40 degrees freezing point and 280 degrees boiling point.
the number of degrees between freezing point and boiling point for smith is 100 degrees.
the number of degrees between freezing point and boiling point for jones is 240 degrees.
each increment on the jones scale is 240 / 100 = 2.4 times each increment on the smith scale.
to make the freezing point the same, you need to adjust the jones scale by -20.
consider freezing point for smith is 25 degrees and freezing point for jones is 40.
since jones increment is 2.4 * smith, then you get:
jones freezing point is 25 * 2.4 = 60 - 20 = 40.
jones scale is equal to smith scale by the formula of j = s * 2.4 - 20.
while the in between may not be exact if the change in degrees is not linear, the freeze and boil points should be right on.
when smith = 25 degrees, jones = 25 * 2.4 - 20 = 40.
their freeze points are consistent with what each is supposed to be.
when smith = 125 degrees, jones = 125 * 2.4 - 20 = 280.
their boiling points are consistent with what each is supposed to be.
therefore, to convert from smith scale to jones scale, your formula is j = 2.4 * s - 20
to convert from jones scale to smith scale, your formula is s = (j + 20) / 2.4
at the freezing point, you have s = 25 and j = 40.
when you convert from s to j, you get j = 2.4 * s - 20 = 2.4 * 25 - 20 = 40.
when you convert from j to s, you get s = (j + 20) / 2.4 = (40 + 20) / 2.4 = 60 / 2.4 = 25
at the boiling point, you have s = 125 and j = 280.
when you convert from s to j, you get j = 2.4 * 125 - 20 = 280.
when you convert from j to s, you get s = (280 + 20) / 2.4 = 125.
if your problem is not what i described above, then i have no idea what you would do.
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