Question

Water freezes at 32 °F or at 0 °C . Also, –40 °C and –40 °F describe the same temperature.
If the Celsius and Fahrenheit scales of temperature are related through the given equation, what would 122 °F in Celsius be?

$Celsius=A(Fahrenheit–B)$

• A. 100°
• B. 75°
• C. 50°
• D. 25°

Answer 1

The correct option is C 50°

Water freezes at 0 °C.

Given: Water freezes at 32 °F.

$⟹0°C=A(32°F–B)⟹B=32$

So, the equation can rewritten as:

$Celsius=A(Fahrenheit–2)$

We also know that

$–40°C=–40°F$

$⟹Celsius=A(Fahrenheit–32)⟹–40°C=A(–40°F–32°F)⟹–40°C=A(–72°F)⟹A=\frac{40}{72}⟹A=\frac{5}{9}$

So, the equation can be expressed as:

$Celsius=\frac{5}{9}(Fahrenheit–32)$

Now, calculating 122 °F in Celsius, we find:

$Celsius=\frac{5}{9}(Fahrenheit–32)=\frac{5}{9}(122°F–32°F)=\frac{5}{9}\left(90\right)=50°C$