Olivia has some caramel apples and mochi balls. If she packs a caramel apple and a mochi ball in each bag, there will be 16 mochi balls left. If she packs 3 caramel apples and 4 mochi balls in each bag, there will be 24 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 + 16	3 p + 24	4 p
Change	- 1 u	- 1 u	- 3 p	- 4 p
After	0	16	24	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 = 3 p + 24 --- (1)

1 u + 16 = 4 p
1 u = 4 p - 16 --- (2)

(2) = (1)
4 p - 16 = 3 p + 24
4 p - 3 p = 24 + 16

1 p = 40

Total number of caramel apples and mochi balls
= (3 p + 24) + 4 p
= 7 p + 24
= 7 x 40 + 24
= 280 + 24
= 304

Answer(s): 304