A faulty thermometer reads 2^ C in melting ice and 92^ C in boiling water. The true temperature on the Celsius scale at which this faulty thermometer gives the exact same numerical reading is ______ ^ C .

Step-by-step solution

Let the temperature at which both the faulty thermometer and the correct Celsius thermometer show the same numerical reading be T . Using the relation between the two scales: T_ faulty - LFP UFP - LFP = T_ true - 0 100 - 0 Substitute the known values and set T_ faulty = T_ true = T : T - 2 92 - 2 = T 100 T - 2 90 = T 100 Cross-multiplying gives: 10(T - 2) = 9T 10T - 20 = 9T T = 20^ C Answer: 20