Who Gets a Free Book and Calendar at the Book Sale?

[t3rom]

Homework Statement

Every 6th person who arrives at a book sale receives a free calendar and every 8th person receives a free book. Which of the first 50 people receive a book and a calendar?

Homework Equations

Kindly check and the solution please. Can't really figure it out.

The Attempt at a Solution

Every 14th person a free calendar and book.

 

[BvU]

How did you come to this number 14 ?

 

[t3rom]

It is my son who came up with 14. I'm not good at math unfortunately.

 

[BvU]

Then we do the counting: numbers 6, 12, 18 etc get a calendar.
Numbers 8, 16, etc get a book.

Continue the series and find the folks that get both !
See if there is a way to do it when they ask for the first 1000 customers ...

 

[PeroK]

It is my son who came up with 14. I'm not good at math unfortunately.

I can imagine a good, old argument in the bookstore: "my son was the 14th person in the store, so he wants his fee calendar and his free book".

 

[t3rom]

I came up with 24 and 48. Is this correct? Thanks for helping!

 

[BvU]

That's the idea. Numbers like 24 and 48 can be divided by 8 and by 6.

 

[PeroK]

I came up with 24 and 48. Is this correct? Thanks for helping!

Hopefully the bookstore owner would agree with that and there would be no argument!