To determine the reading in scale X for a temperature of 60°C, we can use the concept of proportionality between Celsius and the unknown scale X.
Given that the ice point on scale X is 50°X and the steam point on scale X is 200°X, we can calculate the proportionality constant (K) using the known temperatures on the Celsius scale.
The difference between the ice point and the steam point on the Celsius scale is 100°C (200°C - 100°C = 100°C). Similarly, the difference between the ice point and the steam point on scale X is 150°X (200°X - 50°X = 150°X).
Now, we can set up a proportion using the known values:
Celsius / 100 = X / 150
Substituting the Celsius value of 60°C:
60 / 100 = X / 150
Simplifying the equation:
0.6 = X / 150
To solve for X, we can multiply both sides of the equation by 150:
0.6 * 150 = X
X ≈ 90
Therefore, a temperature of 60°C would correspond to approximately 90°X on the unknown scale X.