Sara made a batch of cookies. she gave one-quarter of the batch to kevin, one-fifth to katie, and one-sixth to mike. if those three were given a total of 74 cookies, how many cookies were in the original batch.
the answer also an explination why

the number of the cookies in the original batch is 120

Step-by-step 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

1/800 is the right answer