Question

Scientist cindy Grade has developed a new thermometer. Unlike the thermometer developed by Gabriel Fahrenheit were 32°F marks the freezing point in water and 212°F marks the boiling point, Dr. Grades's thermometer reads 0Degreez jeep for freezing point and 150° G for the boiling point. Write a formula that expresses the relationship between the grade scale (G) and the Fahrenheit scale (F). Do the scales ever agree? If so, at what temperature reading?

Answer 1

Explanation:

The two thermometers developed by cindy Grade and Gabriel Fahrenheit are shown in the attached photo

Let x = a certain temperature reading on the Gabriel Fahrenheit's thermometer

Let y = a corresponding temperature reading on the cindy Grade's thermometer

Interpolating the temperatures, it becomes

(212 - 32)/(212 - x) = (150 - 0)/(150 - y)

(212 - 32)(150 - y) = 150(212 - x)

180(150 - y) = 31800 - 150x

2700 - 180y = 31800 - 150x

180y - 150x = 31800 - 27000

180y - 150x = 31800 - 27000

180y - 150x = 4800

The scales will agree at a common reading. This is achieved by making x to equal y. Therefore

180x - 150x = 4800

30x = 4800

x = 4800/30 = 160

At a reading of 160, both scales will agree