Every ninth person in line at a movie theater gets free popcorn. Every sixth person gets free apple juice. Shani says that the thirty-sixth customer to get both free popcorn and free apple juice. Is she right? If not, describe her mistake.

Find the common multiples:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48

Multiples of 9: 9, 18, 27, 36, 45

The common multiples are 18 and 36

The first person in line to get both free would be the 18th person and then the 36th person.

So she is correct that the 36th person would get both free, but they wouldn't be the first person to do it.