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Ch.1 - Matter, Measurement & Problem Solving
Chapter 1, Problem 109

Suppose you design a new thermometer called the X thermometer. On the X scale, the boiling point of water is 130 °X, and the freezing point of water is 10 °X. At what temperature are the readings on the Fahrenheit and X thermometers the same?

Verified step by step guidance
1
<insert step 1> Determine the relationship between the X scale and the Celsius scale. The freezing point of water is 0 °C and corresponds to 10 °X, while the boiling point of water is 100 °C and corresponds to 130 °X.>
<insert step 2> Calculate the conversion factor between the X scale and the Celsius scale. Use the formula: (X - 10) / (130 - 10) = (C - 0) / (100 - 0).>
<insert step 3> Solve the equation from step 2 to express the temperature in Celsius (C) in terms of the temperature in X (X).>
<insert step 4> Use the relationship between Celsius and Fahrenheit: F = (9/5)C + 32. Substitute the expression for C from step 3 into this equation to express F in terms of X.>
<insert step 5> Set the expression for F equal to X to find the temperature at which the Fahrenheit and X readings are the same. Solve for X.>