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$C \ = \ \frac{5}{9}(F-32)$

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?

Eleftheria Chatziargyriou
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Stevo
  • 241

1 Answers1

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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

Cecilia Cheruto
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