Please 3

Please help; I'm lost! I'm calculating the difference between two Fahrenheit degrees 55°F - 37°F = 18 °F
Now, if I convert the degrees Fahrenheit to Celsius before subtracting, we get 12.78°C —2.78 =10°C. How is that possible when 18°F does not equal 10°C? Could you please explain?

Correct answer:

d =  18 °F
c =  10 °C
c₂ =  18 °F

Step-by-step explanation:

$$\begin{gathered} t_1=55\text{°F} \\ {t}_2=37\text{°F} \\ d=t_1-t_2=55-37=18\text{°F} \end{gathered}$$

$$\begin{gathered} T_1=(t_1-32)\cdot \frac{5}{9}=(55-32)\cdot \frac{5}{9}=\frac{115}{9}\doteq 12.7778\text{°C} \\ {T}_2=(t_2-32)\cdot \frac{5}{9}=(37-32)\cdot \frac{5}{9}=\frac{25}{9}\doteq 2.7778\text{°C} \\ c=T_1-T_2=\frac{115}{9}-\frac{25}{9}=\frac{115-25}{9}=\frac{90}{9}=10\text{°C} \end{gathered}$$

$c_2=\frac{9}{5}\cdot c=\frac{9}{5}\cdot 10=\frac{9\cdot 10}{5}=\frac{90}{5}=18\text{°F}$

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