Question

A Faulty thermometer reads $5^{\circ }C$ in melting ice and ${99}^{\circ }C$ in steam. Find the correct temperature in ${}^{\circ }F$ when this faulty thermometer reads ${52}^{\circ }C$.

Answer 1

Since the temperature scale is linear,

$\frac{T-5}{99-5}=\frac{F-32}{212-32}$

$F=\frac{180}{94}(T-5)+32$

$F=\frac{180}{94}(52-5)+32={122}^{0}F$

Answer is ${122}^{0}F$