Question

At what temperature is the temperature in degrees Fahrenheit equal to twice the temperature in degrees Celsius?

Short answer

The temperature at which the temperature in degrees Fahrenheit is equal to twice the temperature in degrees Celsius is \(320^\circ\text{F}\).

Step-by-step solution

Write the formula for conversion between Celsius and Fahrenheit

The formula to convert Celsius to Fahrenheit is given by: \(F = \frac{9}{5}C + 32\), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius.

Set up the equation

We are given that the temperature in degrees Fahrenheit (F) is equal to twice the temperature in degrees Celsius (2C). So, we can set up the equation: \(F = 2C\).

Substitute the conversion formula into the equation

Now, we will substitute the conversion formula from Step 1 into the equation from Step 2: \(\frac{9}{5}C + 32 = 2C\).

Solve for the temperature in Celsius

We will solve the equation for C to find the temperature in Celsius: \[\begin{aligned} \frac{9}{5}C + 32 &= 2C \\ \frac{9}{5}C - 2C &= -32 \\ \frac{-1}{5}C &= -32 \end{aligned} \] Now, we will multiply both sides by -5 to find the value of C: \[C = 160\]

Convert back to Fahrenheit

We found the temperature in Celsius at which Fahrenheit is twice the value of Celsius. Now, we will convert the Celsius value back to Fahrenheit using the formula from Step 1: \[F = \frac{9}{5}(160) + 32 = 320\] So, the temperature at which the temperature in degrees Fahrenheit is equal to twice the temperature in degrees Celsius is 320°F.