$C \ = \ \frac{5}{9}(F-32)$
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $\frac{5}{9}$ degree Celsius
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III. A temperature increase of $\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only B) II only C) III only D) I and II only
I can only say that $I \ = \ C \ = \ \frac{5*1}{9} \ = \ \frac{5}{9}$ so I is true. But is II and III true? If it is, what is the answer?
Is A) the answer?
Given C= 5/9(F−32) Making F the subject of the formula F= 9/5 C+32 If F' = F + 1 C′= 5/9(F′−32) Substituting with the value of F' C′= 5/9(F+1−32) C'= 5/9(F−32)+ 9/5×1 C′= C+5/9 A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius. Statement I is true.
If C' = C+1 F′= 9/5 C′+32 F′= 9/5(C+1)+32 F′=(9/5 C+32)+ 9/5 F′=F+9/5 F′=F+1.8 A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit. Statement II is true.
If F′=F+ 5/9 C′= 5/9(F′−32) C′= 5/9(F+ 5/9−32) C′= 5/9(F−32)+ 5/9 × 5/9 C′=C+ 25/81 Hence, a temperature increase of
9/5 degree Fahrenheit is equivalent to a temperature increase of
25/81 degree Celsius. Statement III is false.
Therefore D is the answer. Here is a resource to read further about degrees Fahrenheit and degree Celsius