There are some cupcakes in a box. The cupcakes can be put into plates of 2 or 4 with no cupcakes leftover. When the cupcakes are put into plates of 9, there are short of 7 cupcakes on the last plate. If there are more than 50 cupcakes but less than 70 cupcakes, how many cupcakes are there in the box?
If cupcakes can be put into plates of 2 or 4 with no cupcakes leftover, the number of cupcakes is a multiple of 4 as 4 is a multiple of 2.

Multiples of 4 that are greater than 50 but less than 70: 52, 56, 60, 64, 68

Multiples of 9 that are greater than 50 but less than 70: 54, 63
Multiples of 9 (- 7) that are greater than 50 but less than 70: 47, 56

Common number = 56

Number of cupcakes = 56

Answer(s): 56