Dr B's Temperature

Let the measurement in B-scale be $y$ and that in Celsius be $x$ . Assuming the B-scale is linear just as the Celsius scale, the transformation formula is as follows:

$\begin{aligned} y & = mx + c & \small \color{#3D99F6} \text{where }m \text{ and }c \text{ are constants.} \\ - 1000 & = (0)m + c & \small \color{#3D99F6} \text{when }x=0, y = -1000 \\ \implies c & = -1000 \\ 1000 & = 100m - 1000 & \small \color{#3D99F6} \text{when }x=100, y = 1000 \\ \implies m & = 20 \\ \implies y(x) & = 20x - 1000 & \small \color{#3D99F6} \text{Putting }x=25 \\ y(25) & = 20(25) - 1000 \\ & = \boxed{-500} \end{aligned}$

In C scale, 25 is 1/4 of the way from freezing to boiling whicj is 0 to 100. So in B scale, we should be 1/4 of the way from -1000 to + 1000 = - 500. Ed Gray

The freezing point of water is $0°\text{C}$ and the boiling point of water is $100°\text{C}$ . So $0°\text{C} = -1000°\text{B}$ and $100°\text{C} = 1000°\text{B}$ .

Expressing these as coordinate points $(C, B)$ we have $(0, -1000)$ and $(100, 1000)$ . The slope between these two points is $m = \frac{1000 - (-1000)}{100 - 0} = 20$ . Assuming a linear relationship, $B = 20C - 1000$ .

Therefore, $25°\text{C}$ is $B = 20(25) - 1000 = \boxed{-500}°\text{B}$ .

Temperature is a physical quantity which by it's very nature ,doesn't span across various orders of magnitude. This is due to the fact that the Homo sapiens do not deal with a large temperature range in their day-to-day lives. To suit such requirements, a linear scale suffices thus Celsius, Fahrenhiet and Kelvin scales are linear. Extending this to Dr Brilliant's scale , we assume it is also linear.

Therefore the first step over here would be to find a conversion scale between Celsius and Dr Brilliant Scale. I know a graph is not really needed but it actually makes things clear to find an equation determining the conversion relationship.

The equation of a linear graph is in the form of $y=mx+c$ . We know that c is the y intercept while m is the gradient.

From the above graph , we can clearly see that c = -1000. So now we need to find m.

So now we can form the final equation

$y= 20x-1000$ where $x= Temperature in Celsius$ $y = Temperature in Brilliant$

Now substituting the value x=25 celsius gives us

$y = 20 (25) -1000 = 500 -1000 = -500 B$

Hope I helped