Xandra has some chocolate bars and mochi balls. If she packs a chocolate bar and a mochi ball in each bag, there will be 22 mochi balls left. If she packs 5 chocolate bars and 6 mochi balls in each bag, there will be 29 chocolate bars left. How many chocolate bars and mochi balls does she have in all?

	Case 1		Case 2
	Chocolate Bars	Mochi Balls	Chocolate Bars	Mochi Balls
Before	1 u	1 u + 22	5 p + 29	6 p
Change	- 1 u	- 1 u	- 5 p	- 6 p
After	0	22	29	0

The number of chocolate bars 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 = 5 p + 29 --- (1)

1 u + 22 = 6 p
1 u = 6 p - 22 --- (2)

(2) = (1)
6 p - 22 = 5 p + 29
6 p - 5 p = 29 + 22

1 p = 51

Total number of chocolate bars and mochi balls
= (5 p + 29) + 6 p
= 11 p + 29
= 11 x 51 + 29
= 561 + 29
= 590

Answer(s): 590