One winter night the temperature fell degrees between midnight and 5 A.M. By 9 A.M.the temperature had doubled from what it was at 5 A.M. By noon, it had risen another degrees to degrees. What was the temperature at midnight?

Question

One winter night the temperature fell  degrees between midnight and 5 A.M. By 9 A.M.the temperature had doubled from what it was at 5 A.M. By​ noon, it had risen another  degrees to  degrees. What was the temperature at​ midnight?

Mercury · Answer

Full problem (please correct me if this is wrong)

One winter night the temperature fell 15 degrees between midnight and 5am. By 9am, the temperature had doubled from what is was at 5am. By noon, it had risen another 10 degrees to 32 degrees. What was the temperature at midnight?

Mercury · Answer

we'll need to work backwards, starting with the temperature at noon

if the temperature rose 10 degrees, and ended up at 32 degrees at noon, it stands to reason that the temperature before noon was 32 - 10 = 22

working backwards from 22 degrees, if the temperature doubled by 9am, then the temperature must have been half of 22 before 9am

finally, if it fell 15 degrees between midnight and 5am, then the midnight temperature must have been 15 degrees higher than the previous temperature

with all the calculations done, what's your result?