Hilda and Kathy have some biscuits each. If Hilda gives Kathy 38 biscuits, Hilda will have ¹₂ as many biscuits as Kathy. If Hilda gives Kathy 9 biscuits, they will have an equal number of biscuits. How many biscuits does Kathy have at first?

	Case 1		Case 2
	Hilda	Kathy	Hilda	Kathy
Before	1 u + 38	2 u - 38	1.5 u + 9	1.5 u - 9
Change	- 38	+ 38	- 9	+ 9
After	1 u	2 u	1.5 u	1.5 u

Total number of biscuits that Hilda and Kathy have
= 1 u + 2 u
= 3 u 

Number of biscuits that Hilda and Kathy each has in the end is the same.

Number of biscuits that Hilda and Kathy each has in the end in Case 2
= 3 u ÷ 2
= 1.5 u

Number of biscuits that Hilda had at first is the same in Case 1 and Case 2.

1.5 u + 9 = 1 u + 38
1.5 u - 1 u = 38 - 9
0.5 u = 29

1 u = 29 ÷ 0.5 = 58

Number of biscuits that Kathy has
= 2 u - 38
= 2 x 58 - 38
= 116 - 38
= 78

Answer(s): 78