The linear equation that converts Fahrenheit (F) to Celsius (C ) is given by the relation, `C=(5F-160)/(9)`.
(i) If the temperature is `86^(@)` F , what is the temperature in Celsius ?
(ii) If the temperature is `35^(@)`C, what is the temperature in Fahrenheit ?
(iii) If the temperature is `0^(@)`C, what is the temperature in Fahrenheit and if the temperature is `0^(@)`F, what is the temperature in Celsius ?
(iv) What is the numerical value of the temperature which is same in both the scales ?

Explanation

Given relation is , `C=(5F-160)/(9)`
`implies " " 9C=5F-160 implies 5F=9C+160`
`implies " " F=(9C+160)/(5)`
(i) Given, `F=86^(@)F`, then from Eq. (i), we get
`C=(5xx86-160)/(9)=(430-160)/(9)=(270)/(9)=30^(@)C`
(ii) Given, `C=35^(@)C`, then from Eq. (ii), we get
`F=(9xx35+160)/(5)=(315+160)/(5)=(475)/(5)=95^(@)F`
(iii) Given, `C=0^(@)C`, then from Eq. (ii), we get
`F=(9xx0+160)/(5)=(160)/(5)=32^(@)F`
`F=0^(@)F`, then from Eq. (i), we get
`C=(5xx0-160)/(9)=(-160)/(9)=(-(160)/(9)).^(@)C`
(iv) By given condition, C=F
Put this value in Eq. (i), we get
`C=(5C-160)/(9) implies 9C=5C- 160`
`implies 9C- 5C= - 160`
`implies 4C= - 160 implies C= (-160)/(4) implies C = - 40 = F`