Xandra and Fanny have some shortbreads each. If Xandra gives Fanny 34 shortbreads, Xandra will have ⁶₇ as many shortbreads as Fanny. If Xandra gives Fanny 5 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Fanny have at first?

	Case 1		Case 2
	Xandra	Fanny	Xandra	Fanny
Before	6 u + 34	7 u - 34	6.5 u + 5	6.5 u - 5
Change	- 34	+ 34	- 5	+ 5
After	6 u	7 u	6.5 u	6.5 u

Total number of shortbreads that Xandra and Fanny have
= 6 u + 7 u
= 13 u 

Number of shortbreads that Xandra and Fanny each has in the end is the same.

Number of shortbreads that Xandra and Fanny each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u

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

6.5 u + 5 = 6 u + 34
6.5 u - 6 u = 34 - 5
0.5 u = 29

1 u = 29 ÷ 0.5 = 58

Number of shortbreads that Fanny has
= 7 u - 34
= 7 x 58 - 34
= 406 - 34
= 372

Answer(s): 372