Because of an incredibly difficult test , a professor decides to rescale the scores so that the maximum possible is still 100 for a perfect paper, but the average is to be rescales to 75 , instead of it being left at 62.

A. Find a linear Function that represents this scaling. ( the newly revised score should be states as a function of the original score.)

B. If 60 on the new scale is the lowest passing mark, what grade does this correspond to as lowest passing mark on the original scale ?

I believe there are many possible solutions to this.

One possible solution would be f(x) = x + 13 * (100-x)/38 although lower orignal scores like 20% change more drasticaly than higher original scores like 80%.