South African Mathematics Olympiad Second Round

Question

Water freezes at 0^ Celsius and boils at 100^ Celsius. On the SAMO scale, water freezes at 20^ and boils at 170^. The two scales are linearly related. What is the temperature on the SAMO scale if it is 80^ on the Celsius scale?

Accepted Answer

A temperature of 80^ C is 80% of the distance from freezing point to boiling point, so on the SAMO scale the reading is 20 + 80100(170 - 20) = 20 + 120 = 140^.