Question

Suppose you have designed a new thermometer called the X thermometer. On the X scale the boiling point of water is 135 ∘X and the freezing point of water is 11 ∘X. At what temperature on the new X thermometer will the readings on the Fahrenheit and X thermometers be the same? Give answer in X degrees.

Answer 1

Boiling point (BP) of water in fahrenheit = 212 oF

Freezing point (FP) of water in fahrenheit = 32 oF

( F - BP IN F ) / ( BP IN F - FP IN F ) = ( X - BP IN X ) / ( BP IN X - FP IN X )

(F - 212) / (212 - 32) = (X - 135 ) / (135 - 11)

(F - 212) / 180 = (X - 135 ) / 124

180 (X - 135 ) = 124 (F-212)

180 X - 24300 = 124 F - 26288

180X - 124F = -1988

If both are equal then X = F. So,

180 F - 124 F = -1988

56F= -1988

F= -35.5

Answer: F= -35.5

step 1:

get boiling point of water and freezing point of water in F scale

BP(F) = 212 F

FP(F) = 32 F

step 2:

form a equation involving F and X and get relation between F and X

( F - BP(F) ) / ( BP(F) - FP(F) ) = ( X - BP(X) ) / ( BP(X) - FP(X) )

(F - 212) / (212 - 32) = (X - 135 ) / (135 - 11)

(F - 212) / 180 = (X - 135 ) / 124

180 (X - 135 ) = 124 (F-212)

180 X - 24300 = 124 F - 26288

180X - 124F = -1988

step 3:

Put F=X as both are equal

180 X - 124 X = -1988

56X = -1988

X= -35.5

Answer: -35.5 oX