Victoria and Gillian have some puffs each. If Victoria gives Gillian 31 puffs, Victoria will have ²₃ as many puffs as Gillian. If Victoria gives Gillian 8 puffs, they will have an equal number of puffs. How many puffs does Gillian have at first?

	Case 1		Case 2
	Victoria	Gillian	Victoria	Gillian
Before	2 u + 31	3 u - 31	2.5 u + 8	2.5 u - 8
Change	- 31	+ 31	- 8	+ 8
After	2 u	3 u	2.5 u	2.5 u

Total number of puffs that Victoria and Gillian have
= 2 u + 3 u
= 5 u 

Number of puffs that Victoria and Gillian each has in the end is the same.

Number of puffs that Victoria and Gillian each has in the end in Case 2
= 5 u ÷ 2
= 2.5 u

Number of puffs that Victoria had at first is the same in Case 1 and Case 2.

2.5 u + 8 = 2 u + 31
2.5 u - 2 u = 31 - 8
0.5 u = 23

1 u = 23 ÷ 0.5 = 46

Number of puffs that Gillian has
= 3 u - 31
= 3 x 46 - 31
= 138 - 31
= 107

Answer(s): 107