Solve for Equal & Opposite Fahrenheit & Celsius Temperatures

[Imparcticle]

#1) At what temperature are the Fahrenheit and Celsius temperatures exactly equal?

In order to answer this question, I set the following equal:
(the asterisk represents the degree sign)
*F = 1.8 (*C) + 32
*C = ((*F) - 32)/1.8

1.8 (*C) + 32 = ((*F) - 32)/1.8
1.8 (*C) = *F

And I know this is incorrect. Please tell me how to do this.

#2) At what temperature are the Fahrenheit and Celsius temperatures the same value but opposite in sign?

I have no idea how to do this one let alone the previous one. please help.

 

[Atomos]

For question 1: Isolate either C or F in one of the equations, then you can equate your other equation which will represent one of the temperatures to the formula you just derived, and they will both be in terms of the same single variable so it can be solved.

For question 2: same deal, just multiply one of the sides by -1 before you solve.

 

[jamesrc]

Let's start by writing the function for converting between F and C as:
$$f = 1.8c+32$$

f and c are just numbers; we are looking for when f = c in the first question, so substitute in

$$c=1.8c+32$$

and solve.

For the second one, do it the same way except this time you substitute f=-c

 

[Imparcticle]

So would I do this:
for #1:
c=1.8c+32
c-1.8c=32
.8c=32
c=40

#2) -c=1.8(c)+32
-c-1.8c=32
-2.8c=32
c=-11

 

[Diane_]

You lost a minus sign on 1 - try it again.

The other looks fine.