Question

A solution in kept between 68°F and 77°F. What is the range of temperature in degree celsius (C), if the Celsius/Fahrenheit (F) conversion formula is F = `9/5` C + 32?

Answer 1

Temperature range in Fahrenheit:

68^∘F < F < 77^∘F

conversion formula:

F = `9/5` C + 32

the inequality for Celsius

`68< 9/5 C +32<77`

Subtract 32 from all parts

`68-32<9/5C < 77-32`

⇒ 36 < `9/5`C < 45

Multiply by `5/9`

`5/9(36) < C< 5/9(45)`

⇒ 20 < C < 25

20^∘ C < C < 25^∘ C​