Diana has some chocolate bars and candy canes. If she packs a chocolate bar and a candy cane in each bag, there will be 27 candy canes left. If she packs 3 chocolate bars and 4 candy canes in each bag, there will be 14 chocolate bars left. How many chocolate bars and candy canes does she have in all?

	Case 1		Case 2
	Chocolate Bars	Candy Canes	Chocolate Bars	Candy Canes
Before	1 u	1 u + 27	3 p + 14	4 p
Change	- 1 u	- 1 u	- 3 p	- 4 p
After	0	27	14	0

The number of chocolate bars at first is the same for Case 1 and 2.
The number of candy canes at first is also the same for Case 1 and 2.

1 u = 3 p + 14 --- (1)

1 u + 27 = 4 p
1 u = 4 p - 27 --- (2)

(2) = (1)
4 p - 27 = 3 p + 14
4 p - 3 p = 14 + 27

1 p = 41

Total number of chocolate bars and candy canes
= (3 p + 14) + 4 p
= 7 p + 14
= 7 x 41 + 14
= 287 + 14
= 301

Answer(s): 301