Question

the temperature in degrees fahrenheit, f, is related to the temperature in degrees celsius, c, which is represented by the equation $f = \frac{9}{5}c + 32$. there is one temperature where the degrees fahrenheit and degrees celsius are the same, so that $c = f$. what is that temperature?

Explanation:

Step1: Substitute \( F = C \) into the equation

Given \( F=\frac{9}{5}C + 32 \) and \( C = F \), substitute \( F \) with \( C \) in the first equation:
\( C=\frac{9}{5}C + 32 \)

Step2: Solve for \( C \)

Subtract \( \frac{9}{5}C \) from both sides:
\( C-\frac{9}{5}C=\frac{9}{5}C + 32-\frac{9}{5}C \)
\( \frac{5}{5}C-\frac{9}{5}C=32 \)
\( -\frac{4}{5}C = 32 \)

Multiply both sides by \( -\frac{5}{4} \):
\( -\frac{5}{4}\times(-\frac{4}{5}C)=32\times(-\frac{5}{4}) \)
\( C=-40 \)

Answer:

\(-40\) (degrees, since it can be either Celsius or Fahrenheit here as \( C = F \))