If the number of remaining syringes used at night was 1/3 of the number that Dr. Malcolm started with, then the total of the number used during the morning and afternoon was 2/3 of the total.
Let s be the total number of syringes that Dr. Malcolm started with.
number of syringes used in the morning = 0.25s = s/4
number of syringes used ion the afternoon = 45
s/4 + 45 = 2s/3
Multiply both sides by 12:
3s + 540 = 8s
5s = 540
s = 108
Dr. Malcolm started with 108 syringes.