Question

the Fahrenheit and kelvin scales of temperature will give the same reading at

Answer 1

To convert Celsius into Kelvin we can use the formula:
K = C + 273.2 . . . . . . . ..(1)

To convert Fahrenheit into Kelvin we use the formula:
F = (9/5)C + 32 . . . . . . . (2)

At certain temperature, if the "K" & "F" readings are the same,
K° = F°
C + 273.2 = (9/5)C + 32
273.2 - 32 = (9/5)C - C
241.2 = .8C
C = 241.2 / .8 = 301.5

Substitute this value in equations (1) & (2)
K = 301.5 + 273.2 = 574.7°
F = (9/5) 603 + 273.2 = 574.7°

At this temperature, both the thermometers will read the same when kept at the same substance.

Answer 2

574.5875 °F = 574.5875 K (which is the same temperature as 301.4375 °C).