What is the temperature where degrees Fahrenheit and degrees Celsius are the same?
Understand the Problem
The question is asking to find the temperature at which the Fahrenheit and Celsius scales are equivalent. This involves setting the two temperature values equal to one another and solving for the temperature.
Answer
The temperature at which degrees Fahrenheit and degrees Celsius are the same is $C = -40$.
Answer for screen readers
The temperature where degrees Fahrenheit and degrees Celsius are the same is $C = -40$.
Steps to Solve
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Set the temperatures equal To find the temperature where Fahrenheit equals Celsius, set $C = F$.
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Substitute into the equation Using the relationship $F = \frac{9}{5}C + 32$, replace $F$ with $C$: $$ C = \frac{9}{5}C + 32 $$
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Isolate terms Rearranging the equation gives: $$ C - \frac{9}{5}C = 32 $$
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Combine like terms This simplifies to: $$ \left(1 - \frac{9}{5}\right)C = 32 $$ Converting $1$ to a fraction gives: $$ \left(\frac{5}{5} - \frac{9}{5}\right)C = 32 $$ Resulting in: $$ -\frac{4}{5}C = 32 $$
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Solve for C Now, multiply both sides by $-\frac{5}{4}$: $$ C = 32 \times -\frac{5}{4} $$
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Calculate the final value Calculating gives: $$ C = -40 $$
The temperature where degrees Fahrenheit and degrees Celsius are the same is $C = -40$.
More Information
The temperature of -40 degrees is a unique point where both the Celsius and Fahrenheit scales meet, illustrating an interesting equivalence in temperature measurement.
Tips
- Neglecting to set $F$ equal to $C$: Always remember to equate the two scales directly.
- Incorrect manipulation of fractions: Be careful when combining and simplifying fractions to ensure correct arithmetic operations.
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