SOLUTION: You have decided to patent a new temperature scale, called the C51 unit. The C51 units are not based on water, but rather dichloromethane, CH2Cl2, which melts at -97C and boils at

Question 1156315: You have decided to patent a new temperature scale, called the C51 unit. The C51 units are not based on water, but rather dichloromethane, CH2Cl2, which melts at -97C and boils at 40C. You have decided that on your scale, the freezing point of dichloromethane is +1000 C51 and the boiling point is -1000 C51. Determine the relationship to convert C into C51 and C51 into C.
Please help solve this problem Thank you!
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39627) (Show Source): You can put this solution on YOUR website!
Why so backward?

( C, C51 ) for points ( -97, 1000 ) and ( 40, -1000 ). Is the scale, a linear relationship? Form the equation of the line according to those two points.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You have decided to patent a new temperature scale, called the C51 unit. The C51 units are not based on water, but rather dichloromethane, CH2Cl2, which melts at -97C and boils at 40C. You have decided that on your scale, the freezing point of dichloromethane is +1000 C51 and the boiling point is -1000 C51. Determine the relationship to convert C into C51 and C51 into C.
Please help solve this problem Thank you!
-----
C into C51 :::: (C,C51) is the form of the data
You have two points to work with:: (C,C51)
freeze::(0,-1000)
and C
boil::(100,1000)
-----
Equation form:: f(C) = m*C + b
---
slope = m = (1000-(-1000))/(100-0) = 2000/100 = 20
intercept = b = f(0) = -1000
So, C51(C) = 20C -1000
------
C51 into C
Solve equation above for C to get::
C(C51) = (1/20)C51 + 50
================
Cheers,
Stan H.
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