Xylia has some caramel apples and candy canes. If she packs a caramel apple and a candy cane in each bag, there will be 23 candy canes left. If she packs 4 caramel apples and 5 candy canes in each bag, there will be 10 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 + 23	4 p + 10	5 p
Change	- 1 u	- 1 u	- 4 p	- 5 p
After	0	23	10	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 = 4 p + 10 --- (1)

1 u + 23 = 5 p
1 u = 5 p - 23 --- (2)

(2) = (1)
5 p - 23 = 4 p + 10
5 p - 4 p = 10 + 23

1 p = 33

Total number of caramel apples and candy canes
= (4 p + 10) + 5 p
= 9 p + 10
= 9 x 33 + 10
= 297 + 10
= 307

Answer(s): 307