Answer:
The current temperature on the X scale is 1150 °X.
Step-by-step explanation:
Let is determine first the ratio of change in X linear temperature scale to change in Y linear temperature scale:
[tex]r = \frac{\Delta T_{X}}{\Delta T_{Y}}[/tex]
[tex]r = \frac{325\,^{\circ}X-(-115\,^{\circ}X)}{-25\,^{\circ}Y - (-65.00\,^{\circ}Y)}[/tex]
[tex]r = 11\,\frac{^{\circ}X}{^{\circ}Y}[/tex]
The difference between current temperature in Y linear scale with respect to freezing point is:
[tex]\Delta T_{Y} = 50\,^{\circ}Y - (-65\,^{\circ}Y)[/tex]
[tex]\Delta T_{Y} = 115\,^{\circ}Y[/tex]
The change in X linear scale is:
[tex]\Delta T_{X} = r\cdot \Delta T_{Y}[/tex]
[tex]\Delta T_{X} = \left(11\,\frac{^{\circ}X}{^{\circ}Y} \right)\cdot (115\,^{\circ}Y)[/tex]
[tex]\Delta T_{X} = 1265\,^{\circ}X[/tex]
Lastly, the current temperature on the X scale is:
[tex]T_{X} = -115\,^{\circ}X + 1265\,^{\circ}X[/tex]
[tex]T_{X} = 1150\,^{\circ}X[/tex]
The current temperature on the X scale is 1150 °X.
