There are some cookies in a box. The cookies can be put into plates of 3 or 6 with no cookies leftover. When the cookies are put into plates of 14, there are short of 4 cookies on the last plate. If there are more than 50 cookies but less than 70 cookies, how many cookies are there in the box?
If cookies can be put into plates of 3 or 6 with no cookies leftover, the number of cookies is a multiple of 6 as 6 is a multiple of 3.

Multiples of 6 that are greater than 50 but less than 70: 54, 60, 66

Multiples of 14 that are greater than 50 but less than 70: 56, 70
Multiples of 14 (- 4) that are greater than 50 but less than 70: 52, 66

Common number = 66

Number of cookies = 66

Answer(s): 66