Mary has some caramel apples and mochi balls. If she packs a caramel apple and a mochi ball in each bag, there will be 24 mochi balls left. If she packs 2 caramel apples and 3 mochi balls in each bag, there will be 22 caramel apples left. How many caramel apples and mochi balls does she have in all?

	Case 1		Case 2
	Caramel Apples	Mochi Balls	Caramel Apples	Mochi Balls
Before	1 u	1 u + 24	2 p + 22	3 p
Change	- 1 u	- 1 u	- 2 p	- 3 p
After	0	24	22	0

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

1 u = 2 p + 22 --- (1)

1 u + 24 = 3 p
1 u = 3 p - 24 --- (2)

(2) = (1)
3 p - 24 = 2 p + 22
3 p - 2 p = 22 + 24

1 p = 46

Total number of caramel apples and mochi balls
= (2 p + 22) + 3 p
= 5 p + 22
= 5 x 46 + 22
= 230 + 22
= 252

Answer(s): 252