Jen has some caramel apples and mochi balls. If she packs a caramel apple and a mochi ball in each bag, there will be 27 mochi balls left. If she packs 5 caramel apples and 6 mochi balls in each bag, there will be 14 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 + 27	5 p + 14	6 p
Change	- 1 u	- 1 u	- 5 p	- 6 p
After	0	27	14	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 = 5 p + 14 --- (1)

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

(2) = (1)
6 p - 27 = 5 p + 14
6 p - 5 p = 14 + 27

1 p = 41

Total number of caramel apples and mochi balls
= (5 p + 14) + 6 p
= 11 p + 14
= 11 x 41 + 14
= 451 + 14
= 465

Answer(s): 465