Dana and Emily have some shortbreads each. If Dana gives Emily 31 shortbreads, Dana will have ³₄ as many shortbreads as Emily. If Dana gives Emily 9 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Emily have at first?

	Case 1		Case 2
	Dana	Emily	Dana	Emily
Before	3 u + 31	4 u - 31	3.5 u + 9	3.5 u - 9
Change	- 31	+ 31	- 9	+ 9
After	3 u	4 u	3.5 u	3.5 u

Total number of shortbreads that Dana and Emily have
= 3 u + 4 u
= 7 u 

Number of shortbreads that Dana and Emily each has in the end is the same.

Number of shortbreads that Dana and Emily each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u

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

3.5 u + 9 = 3 u + 31
3.5 u - 3 u = 31 - 9
0.5 u = 22

1 u = 22 ÷ 0.5 = 44

Number of shortbreads that Emily has
= 4 u - 31
= 4 x 44 - 31
= 176 - 31
= 145

Answer(s): 145