Natalie has some mini cupcakes and chocolate bars. If she packs a mini cupcake and a chocolate bar in each bag, there will be 30 chocolate bars left. If she packs 4 mini cupcakes and 5 chocolate bars in each bag, there will be 17 mini cupcakes left. How many mini cupcakes and chocolate bars does she have in all?

	Case 1		Case 2
	Mini Cupcakes	Chocolate Bars	Mini Cupcakes	Chocolate Bars
Before	1 u	1 u + 30	4 p + 17	5 p
Change	- 1 u	- 1 u	- 4 p	- 5 p
After	0	30	17	0

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

1 u = 4 p + 17 --- (1)

1 u + 30 = 5 p
1 u = 5 p - 30 --- (2)

(2) = (1)
5 p - 30 = 4 p + 17
5 p - 4 p = 17 + 30

1 p = 47

Total number of mini cupcakes and chocolate bars
= (4 p + 17) + 5 p
= 9 p + 17
= 9 x 47 + 17
= 423 + 17
= 440

Answer(s): 440