At what temperatures are the readings on the Fahrenheit and Celsius thermometers the same?

Verified step by step guidance

1. Step 1: Understand that the Fahrenheit and Celsius scales intersect at a certain temperature. This is the point where the temperature in Fahrenheit is equal to the temperature in Celsius.
2. Step 2: Recall the formula to convert Fahrenheit to Celsius: $C = \frac{5}{9}(F - 32)$, where C is the temperature in Celsius and F is the temperature in Fahrenheit.
3. Step 3: To find the temperature where Fahrenheit and Celsius are equal, set C equal to F in the conversion formula: $F = \frac{5}{9}(F - 32)$.
4. Step 4: Solve this equation for F. Start by multiplying both sides by 9/5 to get rid of the fraction: $\frac{9}{5}F = F - 32$.
5. Step 5: Rearrange the equation to isolate F on one side. This will give you the temperature at which Fahrenheit and Celsius are equal.

Key Concepts

Temperature Scales

Fahrenheit and Celsius are two different temperature scales used to measure thermal energy. The Celsius scale is based on the freezing point of water at 0 degrees and the boiling point at 100 degrees, while the Fahrenheit scale sets the freezing point at 32 degrees and the boiling point at 212 degrees. Understanding these scales is essential for converting temperatures and finding points of equivalence.

Temperature Conversion Formula

To find the temperature at which the Fahrenheit and Celsius readings are the same, one can use the conversion formula: F = (C × 9/5) + 32. This formula allows for the conversion of Celsius temperatures to Fahrenheit and vice versa, facilitating the identification of the temperature at which both scales yield the same value.

Intersection of Linear Functions

The relationship between Fahrenheit and Celsius can be represented as linear functions, where the two scales intersect at a specific point. By setting the equations for both scales equal to each other, one can solve for the temperature at which they are identical. This concept of finding intersections is fundamental in algebra and helps visualize the relationship between different temperature scales.