Word problem

Question

Water freezes at 0◦ Celsius and 32◦ Fahrenheit and it boils at 100◦C and 212◦F. (a) Find a linear function F that expresses temperature in the Fahrenheit scale in terms of degrees Celsius. Use this function to convert 20◦C into Fahrenheit. (b) Find a linear function C that expresses temperature in the Celsius scale in terms of degrees Fahrenheit. Use this function to convert 110◦F into Celsius. (c) Is there a temperature n such that F(n) = C(n)?

Answer 1

a)  F = (9/5)C + 32  since there are 180 (212-32) gradations on the Fahrenheit scale, the number of such smaller degree units must be multiplied by 180/100, which reduces to 9/5, and THEN the 32 corresponding to the freezing measurement has to be added.  Check this by substituting C = 0 and also C=100 to verify that the corresponding F values are right.

 

Now use as directed (C=20)

 

b)  You can take the formula in a) and SOLVE for F to get the conversion from Fahrenheit to Celsius.

 

c) YES; not an integer, though.