Winnie has some caramel apples and mini cupcakes. If she packs a caramel apple and a mini cupcake in each bag, there will be 19 mini cupcakes left. If she packs 5 caramel apples and 6 mini cupcakes in each bag, there will be 19 caramel apples left. How many caramel apples and mini cupcakes does she have in all?

	Case 1		Case 2
	Caramel Apples	Mini Cupcakes	Caramel Apples	Mini Cupcakes
Before	1 u	1 u + 19	5 p + 19	6 p
Change	- 1 u	- 1 u	- 5 p	- 6 p
After	0	19	19	0

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

1 u = 5 p + 19 --- (1)

1 u + 19 = 6 p
1 u = 6 p - 19 --- (2)

(2) = (1)
6 p - 19 = 5 p + 19
6 p - 5 p = 19 + 19

1 p = 38

Total number of caramel apples and mini cupcakes
= (5 p + 19) + 6 p
= 11 p + 19
= 11 x 38 + 19
= 418 + 19
= 437

Answer(s): 437