Tiffany and Xylia have some shortbreads each. If Tiffany gives Xylia 34 shortbreads, Tiffany will have ¹₈ as many shortbreads as Xylia. If Tiffany gives Xylia 10 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Xylia have at first?

	Case 1		Case 2
	Tiffany	Xylia	Tiffany	Xylia
Before	1 u + 34	8 u - 34	4.5 u + 10	4.5 u - 10
Change	- 34	+ 34	- 10	+ 10
After	1 u	8 u	4.5 u	4.5 u

Total number of shortbreads that Tiffany and Xylia have
= 1 u + 8 u
= 9 u 

Number of shortbreads that Tiffany and Xylia each has in the end is the same.

Number of shortbreads that Tiffany and Xylia each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

Number of shortbreads that Tiffany had at first is the same in Case 1 and Case 2.

4.5 u + 10 = 1 u + 34
4.5 u - 1 u = 34 - 10
0.5 u = 24

1 u = 24 ÷ 0.5 = 48

Number of shortbreads that Xylia has
= 8 u - 34
= 8 x 48 - 34
= 384 - 34
= 350

Answer(s): 350