Math problem fraction Please explain how the answer was found

Question

there was a jar of cookies on the table. First ken came along and ate half the cookies in the jar. Mary cam in the kitchen next and ate one third of the cookies left in the jar. Karen followed next and took three fourths of the remaining cookies. Susan then grabbed one cookie from the jar. which left one cookie left in the jar. how many cookies were In the jar to start with ? 

Answer 1

C - C/2 = C/2 cookies after Ken

C/2 - (1/3)(C/2) = C/2 - C/6 = C/3 cookies left after Mary

C/3 - (3/4)(C/3) = C/3 - 3C/12 = C/3 - C/4 = C/12 cookies left after Karen

 

C/12 - 1 = 1     Susan took 1 cookie from the remainder, leaving 1 in the jar

C/12 = 2

C = 24 cookies originally

 

Check:

 

24 - 12 = 12      in jar after Ken

12 - 12/3 = 8     in jar after Mary 

8 - (3/4)(8)= 2   in jar after Karen

2 - 1 = 1            in jar after Susan