Shannon has some mini cupcakes and mochi balls. If she packs a mini cupcake and a mochi ball in each bag, there will be 27 mochi balls left. If she packs 5 mini cupcakes and 6 mochi balls in each bag, there will be 10 mini cupcakes left. How many mini cupcakes and mochi balls does she have in all?

	Case 1		Case 2
	Mini Cupcakes	Mochi Balls	Mini Cupcakes	Mochi Balls
Before	1 u	1 u + 27	5 p + 10	6 p
Change	- 1 u	- 1 u	- 5 p	- 6 p
After	0	27	10	0

The number of mini cupcakes 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 + 10 --- (1)

1 u + 27 = 6 p
1 u = 6 p - 27 --- (2)

(2) = (1)
6 p - 27 = 5 p + 10
6 p - 5 p = 10 + 27

1 p = 37

Total number of mini cupcakes and mochi balls
= (5 p + 10) + 6 p
= 11 p + 10
= 11 x 37 + 10
= 407 + 10
= 417

Answer(s): 417