Yen and Gwen have some shortbreads each. If Yen gives Gwen 34 shortbreads, Yen will have ¹₈ as many shortbreads as Gwen. If Yen gives Gwen 6 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Gwen have at first?

	Case 1		Case 2
	Yen	Gwen	Yen	Gwen
Before	1 u + 34	8 u - 34	4.5 u + 6	4.5 u - 6
Change	- 34	+ 34	- 6	+ 6
After	1 u	8 u	4.5 u	4.5 u

Total number of shortbreads that Yen and Gwen have
= 1 u + 8 u
= 9 u 

Number of shortbreads that Yen and Gwen each has in the end is the same.

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

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

4.5 u + 6 = 1 u + 34
4.5 u - 1 u = 34 - 6
0.5 u = 28

1 u = 28 ÷ 0.5 = 56

Number of shortbreads that Gwen has
= 8 u - 34
= 8 x 56 - 34
= 448 - 34
= 414

Answer(s): 414