Question

An equation that can be used to convert a temperature, in degrees Fahrenheit ${(}^{\circ }F)$, to a temperature in degrees in Celsius ${(}^{\circ }C)$ is $c=\frac{5}{9}(f-32)$ . For what value is the temperature in ${(}^{\circ }F)$ equal to the temperature in ${(}^{\circ }C)$?

• A. -40
• B. -100
• C. -32
• D. 40

Answer 1

The correct option is A -40

$c=\frac{5}{9}(f-32)$

We need to consider $c=f$
Therefore, we must solve the following system of equations
$c=\frac{5}{9}(f-32)c=fTherefore,f=\frac{5}{9(f-32)}9f=5f-1609f-5f=-1604f=-160f=-40$
Since $f=-40$, it follows that $c=-40$ and so $-{40}^{\circ }F=-{40}^{\circ }C$
The value for which the temperature in ${}^{\circ }F$ is equal to the temperature in ${}^{\circ }Cis-40.$