Explanation:
you see ? the missing piece of information was that the final step increased the temperature by 8 degrees to 16 degrees.
so, now we know the final temperature and can calculate backwards to the midnight temperature.
x = temperature at midnight.
temperature at 5am = x - 16
temperature at 9am = 2×(temperature at 5am) =
= 2×(x - 16)
temperature at noon = temperature at 9am + 8 =
= 2(x - 16) + 8 = 2x - 32 + 8 =
= 2x - 24
and we know now that this final temperature is 16°.
so,
16 = 2x - 24
40 = 2x
x = 20°
the temperature at midnight was 20°.