Answer: the number of the cookies in the original batch is 120
Explanation:
Let x represent the number of cookies that were in the original batch.
She gave one-quarter of the batch to Kevin. This means that the number of cookies given to Kevin is 1/4×x = x/4
She gave one-fifth to Katie. This means that the number of cookies given to Katie is 1/5×x = x/5
She gave one-sixth to Mike.
This means that the number of cookies given to Mike is 1/6×x = x/6
If those three were given a total of 74 cookies, it means that the sum of the cookies given to Kevin, Katie and Mike 74. It is expressed as
x/4 + x/5 + x/6 = 74
Taking 60 as LCM and multiplying through with it, it becomes
15x + 12x + 10x = 4440
37x = 4440
x = 4440/37
x = 120