Lucy has some caramel apples and candy canes. If she packs a caramel apple and a candy cane in each bag, there will be 19 candy canes left. If she packs 3 caramel apples and 4 candy canes in each bag, there will be 29 caramel apples left. How many caramel apples and candy canes does she have in all?

	Case 1		Case 2
	Caramel Apples	Candy Canes	Caramel Apples	Candy Canes
Before	1 u	1 u + 19	3 p + 29	4 p
Change	- 1 u	- 1 u	- 3 p	- 4 p
After	0	19	29	0

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

1 u = 3 p + 29 --- (1)

1 u + 19 = 4 p
1 u = 4 p - 19 --- (2)

(2) = (1)
4 p - 19 = 3 p + 29
4 p - 3 p = 29 + 19

1 p = 48

Total number of caramel apples and candy canes
= (3 p + 29) + 4 p
= 7 p + 29
= 7 x 48 + 29
= 336 + 29
= 365

Answer(s): 365