College

Celsius and Fahrenheit

The formula to convert from Celsius to Fahrenheit is [tex]F = \frac{9}{5}C + 32[/tex]. Use this formula to complete the statements below. Round your answers to the nearest tenth as needed.

- If the temperature is 80 degrees Fahrenheit, that is equivalent to ___ degrees Celsius.

- If the temperature is 35 degrees Celsius, that is equivalent to ___ degrees Fahrenheit.

Answer :

To solve the problem of converting temperatures between Celsius and Fahrenheit, we'll use two formulas:

1. To convert from Fahrenheit to Celsius:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]

2. To convert from Celsius to Fahrenheit:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]

Let's work through the statements using these formulas:

1. If the temperature is 80 degrees Fahrenheit, what is the equivalent in Celsius?

- Start with the formula to convert Fahrenheit to Celsius:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]

- Substitute [tex]\(F = 80\)[/tex] into the formula:
[tex]\[
C = \frac{5}{9} (80 - 32)
\][/tex]

- Calculate the difference:
[tex]\[
C = \frac{5}{9} \times 48
\][/tex]

- Multiply:
[tex]\[
C = \frac{240}{9} \approx 26.7
\][/tex]

So, 80 degrees Fahrenheit is approximately 26.7 degrees Celsius.

2. If the temperature is 35 degrees Celsius, what is the equivalent in Fahrenheit?

- Use the formula to convert Celsius to Fahrenheit:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]

- Substitute [tex]\(C = 35\)[/tex] into the formula:
[tex]\[
F = \frac{9}{5} \times 35 + 32
\][/tex]

- Multiply:
[tex]\[
F = 63 + 32
\][/tex]

- Add:
[tex]\[
F = 95
\][/tex]

Therefore, 35 degrees Celsius is equivalent to 95 degrees Fahrenheit.

These calculations give the following conversions:
- 80 degrees Fahrenheit is approximately 26.7 degrees Celsius.
- 35 degrees Celsius is 95.0 degrees Fahrenheit.

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