Jean has some candy canes and caramel apples. If she packs a candy cane and a caramel apple in each bag, there will be 20 caramel apples left. If she packs 2 candy canes and 3 caramel apples in each bag, there will be 29 candy canes left. How many candy canes and caramel apples does she have in all?

	Case 1		Case 2
	Candy Canes	Caramel Apples	Candy Canes	Caramel Apples
Before	1 u	1 u + 20	2 p + 29	3 p
Change	- 1 u	- 1 u	- 2 p	- 3 p
After	0	20	29	0

The number of candy canes 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 + 29 --- (1)

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

(2) = (1)
3 p - 20 = 2 p + 29
3 p - 2 p = 29 + 20

1 p = 49

Total number of candy canes and caramel apples
= (2 p + 29) + 3 p
= 5 p + 29
= 5 x 49 + 29
= 245 + 29
= 274

Answer(s): 274