Fahrenheit temperature,F, can be found from a Celsius temperature C, using the formula F=1.8C + 32. Write an equation to find the temperature at which

Question

Fahrenheit temperature,F, can be found from a Celsius temperature C, using the formula F=1.8C + 32. Write an equation to find the temperature at which the Fahrenheit and Celsius readings are equal.  Then find that temperature 

Answer 1

X = 1.8X + 32 where X is the fixed temperature

 

0 = 0.8X + 32

 

-32 = 0.8X

 

-320 = 8X 

 

X = -40

 

Check:  F = 1.8 * -40 + 32 = -72 + 32 = -40

   

   Fahrenheit to Celsius by the way is C = 5*(F-32)/9 

 

   So C = 5*(-40-32)/9 = 5*-72/9 = 5*-8 = -40

 

-40 C = -40 F

Answer 2

Let T be the temperature where F = C.  Then

 

C = 1.8C + 32

 

C(1 - 1.8) = 32

 

C = 32/(1 - 1.8) = -40

 

°C = °F only at -40°