What is the difference in Celsius if the temperature difference in Fahrenheit is 30 degrees?

The conversion formula from Celsius ($C$) to Fahrenheit ($F$) is $F = C \times \frac{9}{5} + 32$.
To find the relationship between temperature differences, consider two temperatures $C_1$ and $C_2$ in Celsius, and their corresponding Fahrenheit temperatures $F_1$ and $F_2$.

$$F_1 = C_1 \times \frac{9}{5} + 32$$ $$F_2 = C_2 \times \frac{9}{5} + 32$$

The difference in Fahrenheit is $\Delta F = F_2 - F_1$.

$$\Delta F = \left(C_2 \times \frac{9}{5} + 32\right) - \left(C_1 \times \frac{9}{5} + 32\right)$$ $$\Delta F = C_2 \times \frac{9}{5} - C_1 \times \frac{9}{5}$$ $$\Delta F = (C_2 - C_1) \times \frac{9}{5}$$

Let $\Delta C = C_2 - C_1$.
So, the relationship is:

$$\Delta F = \Delta C \times \frac{9}{5}$$

We are given that the difference on the Fahrenheit scale is $30^\circ\text{F}$, so $\Delta F = 30^\circ\text{F}$.

$$30 = \Delta C \times \frac{9}{5}$$

To find $\Delta C$, multiply both sides by $\frac{5}{9}$:

$$\Delta C = 30 \times \frac{5}{9}$$ $$\Delta C = \frac{150}{9}$$ $$\Delta C = \frac{50}{3}$$ $$\Delta C \approx 16.666...^\circ\text{C}$$

$$\Delta C \approx 16.7^\circ\text{C}$$

The correct option is 16.7 degrees Celsius.