Gem has some mini cupcakes and caramel apples. If she packs a mini cupcake and a caramel apple in each bag, there will be 12 caramel apples left. If she packs 4 mini cupcakes and 5 caramel apples in each bag, there will be 22 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 + 12	4 p + 22	5 p
Change	- 1 u	- 1 u	- 4 p	- 5 p
After	0	12	22	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 = 4 p + 22 --- (1)

1 u + 12 = 5 p
1 u = 5 p - 12 --- (2)

(2) = (1)
5 p - 12 = 4 p + 22
5 p - 4 p = 22 + 12

1 p = 34

Total number of mini cupcakes and caramel apples
= (4 p + 22) + 5 p
= 9 p + 22
= 9 x 34 + 22
= 306 + 22
= 328

Answer(s): 328