At what temperature does specifying Celsius or Fahrenheit not matter?

Question

There is a specific temperature, where if you had a Celsius and a Fahrenheit thermometer, the values on both thermometers would read the same numerical value. Determine the temperature this occurs at.

Answer 1

-40 degrees

Formula for Celsius to Fahrenheit:

1.8C+32=F

We are trying to find the point where:

C=F

This can become a system of equations.

1.8C+32=F

C=F

To solve this system, first we can multiply both sides of the second equation by -1.8. This enables us to cancel the C variable, allowing us to solve for F.

1.8C+32=F

-1.8C=-1.8F

Now we can add the equations and combine like terms, after which we get:

32=-0.8F

Divide both sides by -0.8

-40=F

To solve for C, we can substitute -40 for F in either of the original equations.

-1.8C+32=-40

-1.8C=-72

C=-40

Answer 2

Let F = the temperature in Fahrenheit and C = the temperature in Celsius

The formula for converting Fahrenheit (F) and to Celsius (C) is given in equation 1:

(1) F = 1.8C + 32

The temperature where specifying Celsius or Fahrenheit doesn't matter is the one that is the same on both scales. This is given by equation 2:

(2) F = C

So you have a system of equations you can use to solve for the temperature where F =C. There are a couple of equally good approaches:

1. Substitution. Since F = C you can replace F with C in equation 1, then solve for C
2. Substitution. Since F = C you can replace C with F in equation 1, then solve for F
3. Elimination. Subtract equation 2 from equation 1 to eliminate F, then solve for C

Hope this helps! Just add a comment if you have any questions.