Question

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

Short answer

The temperature at which Fahrenheit is equal to twice the temperature in Celsius is \(160^{\circ}C\).

Step-by-step solution

Write down the given equation

We are given that the temperature in degrees Fahrenheit (F) is equal to twice the temperature in degrees Celsius (C). We can write this as: F = 2C

Convert Celsius to Fahrenheit

Now, we will use the formula to convert degrees Celsius to Fahrenheit: F = (9/5)C + 32. We will substitute this into our equation from Step 1: (9/5)C + 32 = 2C

Solve for C

Now, we will solve for C by isolating the variable on one side of the equation: (9/5)C + 32 = 2C 32 = 2C - (9/5)C 32 = (10/5)C - (9/5)C 32 = (1/5)C Now, we will multiply both sides of the equation by 5 to get rid of the fraction: 5 * 32 = 5 * (1/5)C 160 = C

Check the result

We found that C = 160, so the temperature in degrees Celsius is 160°C. Now, we will plug this value back into the equation F = (9/5)C + 32 to find the temperature in degrees Fahrenheit: F = (9/5)(160) + 32 F = 288 + 32 F = 320 Since 320 is twice 160, our answer is valid, and the temperature at which Fahrenheit is equal to twice the temperature in Celsius is 160°C.