Answer
$73^{\circ}S$
Work Step by Step
First, we need to determine the number of $^{\circ}C$ units there are in the new scale.
We're going from $-117.3^{\circ}C$ to $0^{\circ}C$ and to $78.3^{\circ}C$.
We're going to count the centigrade units, regardless of sign.
$117.3 ^{\circ}C + 78.3^{\circ}C = 195.6^{\circ}C$
Hence, for every $100^{\circ}S$, there are $195.6^{\circ}C$. This will be our unit factor.
However, we need to remember that the melting point was originally lower.
We need to account for this on our calculations and we could do so by adding it to $25^{\circ}C$
$(25+117.3)^{\circ}C \times \frac{100^{\circ}S}{195.6^{\circ}C} = 73^{\circ}S $
