Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other.

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Start by understanding the relationship between the Fahrenheit and Celsius temperature scales. The formula to convert Celsius to Fahrenheit is:

F = \frac{9}{5} C + 32

To find the temperature at which both scales agree, set the Fahrenheit temperature equal to the Celsius temperature:

F = C

Substitute

F = C

into the conversion formula:

C = \frac{9}{5} C + 32

Rearrange the equation to isolate

C

on one side:

C - \frac{9}{5} C = 32

Solve the equation for

C

to find the temperature at which both scales agree.

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주요 개념

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Temperature Scales

Temperature scales are systems for measuring temperature, with Celsius and Fahrenheit being two common ones. Celsius is based on the freezing and boiling points of water, while Fahrenheit uses a different scale. Understanding how these scales relate is crucial for converting temperatures between them.

Conversion Formula

The conversion formula between Celsius and Fahrenheit is F = (C × 9/5) + 32. This formula allows you to convert a temperature from Celsius to Fahrenheit and vice versa. Solving the problem requires setting the two scales equal and finding the temperature where they intersect.

Algebraic Equations

Algebraic equations involve finding unknown values by manipulating mathematical expressions. In this context, setting the Celsius and Fahrenheit conversion formula equal to each other forms an equation that can be solved to find the temperature where both scales agree.