Shiyun has some mini cupcakes and caramel apples. If she packs a mini cupcake and a caramel apple in each bag, there will be 22 caramel apples left. If she packs 5 mini cupcakes and 6 caramel apples in each bag, there will be 16 mini cupcakes left. How many mini cupcakes and caramel apples does she have in all?

	Case 1		Case 2
	Mini Cupcakes	Caramel Apples	Mini Cupcakes	Caramel Apples
Before	1 u	1 u + 22	5 p + 16	6 p
Change	- 1 u	- 1 u	- 5 p	- 6 p
After	0	22	16	0

The number of mini cupcakes at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.

1 u = 5 p + 16 --- (1)

1 u + 22 = 6 p
1 u = 6 p - 22 --- (2)

(2) = (1)
6 p - 22 = 5 p + 16
6 p - 5 p = 16 + 22

1 p = 38

Total number of mini cupcakes and caramel apples
= (5 p + 16) + 6 p
= 11 p + 16
= 11 x 38 + 16
= 418 + 16
= 434

Answer(s): 434