Xuan has some mini cupcakes and caramel apples. If she packs a mini cupcake and a caramel apple in each bag, there will be 10 caramel apples left. If she packs 2 mini cupcakes and 3 caramel apples in each bag, there will be 20 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 + 10	2 p + 20	3 p
Change	- 1 u	- 1 u	- 2 p	- 3 p
After	0	10	20	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 = 2 p + 20 --- (1)

1 u + 10 = 3 p
1 u = 3 p - 10 --- (2)

(2) = (1)
3 p - 10 = 2 p + 20
3 p - 2 p = 20 + 10

1 p = 30

Total number of mini cupcakes and caramel apples
= (2 p + 20) + 3 p
= 5 p + 20
= 5 x 30 + 20
= 150 + 20
= 170

Answer(s): 170