Yoko has some mochi balls and caramel apples. If she packs a mochi ball and a caramel apple in each bag, there will be 27 caramel apples left. If she packs 4 mochi balls and 5 caramel apples in each bag, there will be 22 mochi balls left. How many mochi balls and caramel apples does she have in all?

	Case 1		Case 2
	Mochi Balls	Caramel Apples	Mochi Balls	Caramel Apples
Before	1 u	1 u + 27	4 p + 22	5 p
Change	- 1 u	- 1 u	- 4 p	- 5 p
After	0	27	22	0

The number of mochi balls 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 = 4 p + 22 --- (1)

1 u + 27 = 5 p
1 u = 5 p - 27 --- (2)

(2) = (1)
5 p - 27 = 4 p + 22
5 p - 4 p = 22 + 27

1 p = 49

Total number of mochi balls and caramel apples
= (4 p + 22) + 5 p
= 9 p + 22
= 9 x 49 + 22
= 441 + 22
= 463

Answer(s): 463