Victoria and Gwen have some tarts each. If Victoria gives Gwen 17 tarts, Victoria will have ²₉ as many tarts as Gwen. If Victoria gives Gwen 9 tarts, they will have an equal number of tarts. How many tarts does Victoria have at first?

	Case 1		Case 2
	Victoria	Gwen	Victoria	Gwen
Before	2 u + 17	9 u - 17	5.5 u + 9	5.5 u - 9
Change	- 17	+ 17	- 9	+ 9
After	2 u	9 u	5.5 u	5.5 u

Total number of tarts that Victoria and Gwen have
= 2 u + 9 u
= 11 u 

Number of tarts that Victoria and Gwen each has in the end is the same.

Number of tarts that Victoria and Gwen each has in the end in Case 2
= 11 u ÷ 2
= 5.5 u

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

5.5 u + 9 = 2 u + 17
5.5 u - 2 u = 17 - 9
0.5 u = 8

1 u = 8 ÷ 0.5 = 16

Number of tarts that Victoria has
= 2 u + 17
= 2 x 16 + 17
= 32 + 17
= 49

Answer(s): 49