### Question

What is the temperature at which Fahrenheit and Celsius thermometer readings are equal?

Asked by: Hamid A. Khan

### Answer

**The temperature at which Fahrenheit and Celsius thermometer readings are equal is: - 40 degrees.**

Well if you look at the conversion formulas for Celsius to Fahrenheit, or that of Fahrenheit
to Celsius, you can manipulate it mathematically to answer this question.

The conversion formula reads:

**T(F) = T(C) x 9/5 + 32**

this means that the temperature of Fahrenheit equals the temperature of Celsius multiplied
by nine / fifths, plus 32 degrees.

If the temperatures are the same then the two 'T's' in the formula should represent the
same temperature.

So,

**t = t x 9/5 + 32**

minus the nine fifths of t from each side to move it to the left of the equation.
this leaves:

t - 9t/5 = 32 ------> this leaves: - 4t/5 = 32

so then you multiply each side by - 5/4 to solve for t, and you get** t = - 40 degrees**!

(by the way, 't' times,(x), nine/fifths equals 9t/5)

Answered by: Dominic Jones, D.B., High School Student