Question

step-by-step solution where ℉ = ℃

Answer 1

What we know:
Fahrenheit to Celsius
℉ = (9℃/5) + 32
Celsius to Fahrenheit
℃ = (F-32)
----------------------

F = (9C/5) + 32
F = C
C = (9C/5) + 32
Let us combine terms that are alike. We achieve that by subtracting 9C/5 on both sides of the equation.
C - 9C/5 = 32
Perform the operation.
5C/5 - 9C/5 = 32
-4C/5 = 32
We solve for C by multiplying both sides of the equations by 5, and then dividing them by -4.
-4C/5 * 5 = 32 * 5
-4C = 160
-4C ÷ -4 = 160 ÷ 4
C = -40

Check:
Convert -40℃ to Fahrenheit
-40* 9 ÷ 5 + 32
-360 ÷ 5 + 32
-72 + 32
-40

Answer 2

This problem came up several times here on openstudy and then I encountered it again recently.

Answer 3

your sarcasm is very subtle @Luis_Rivera I almost cannot tell...

Answer 4

I would just answer those questions with this:
\[F = \frac{9}{5}C+ 32\]\[C = \frac{5}{9}(F-32)\]\[C=F\]\[C-F=0\]\[(\frac{5}{9} (x-32))-(\frac{9}{5}x+32)=0\]\[x=-40\]