Question

At what temperature does the numerical value in °F match the numerical value in °C?

Answer 1

Answer: -40

The formula to convert
`\ºC` to
`\ºF` is:

`\ºF=(9)/(5)\ºC+32` (1)

and to convert
`\ºF` to
`\ºC` is:

`\ºC=(\ºF-32)(9)/(5)` (2)

Now, if we want to know at what temperature does the numerical value in
`\ºF` match the numerical value in
`\ºC`, we have to make
`\ºC=\ºF` and solve any of both equations shown above.

Using (1):

`\ºC=(9)/(5)\ºC+32`

`\ºC-(9)/(5)\ºC=32`

`-(4)/(5)\ºC=32`

`\ºC=-40`

Using (2):

`\ºC=(\ºC-32)(9)/(5)`

`\ºC-(5)/(9)\ºC=-(160)/(9)`

`\ºC=-40`