Victoria has some chocolate bars and mini cupcakes. If she packs a chocolate bar and a mini cupcake in each bag, there will be 23 mini cupcakes left. If she packs 4 chocolate bars and 5 mini cupcakes in each bag, there will be 29 chocolate bars left. How many chocolate bars and mini cupcakes does she have in all?

	Case 1		Case 2
	Chocolate Bars	Mini Cupcakes	Chocolate Bars	Mini Cupcakes
Before	1 u	1 u + 23	4 p + 29	5 p
Change	- 1 u	- 1 u	- 4 p	- 5 p
After	0	23	29	0

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

1 u = 4 p + 29 --- (1)

1 u + 23 = 5 p
1 u = 5 p - 23 --- (2)

(2) = (1)
5 p - 23 = 4 p + 29
5 p - 4 p = 29 + 23

1 p = 52

Total number of chocolate bars and mini cupcakes
= (4 p + 29) + 5 p
= 9 p + 29
= 9 x 52 + 29
= 468 + 29
= 497

Answer(s): 497