Pamela and Sarah have some biscuits each. If Pamela gives Sarah 36 biscuits, Pamela will have ⁷₈ as many biscuits as Sarah. If Pamela gives Sarah 8 biscuits, they will have an equal number of biscuits. How many biscuits does Sarah have at first?

	Case 1		Case 2
	Pamela	Sarah	Pamela	Sarah
Before	7 u + 36	8 u - 36	7.5 u + 8	7.5 u - 8
Change	- 36	+ 36	- 8	+ 8
After	7 u	8 u	7.5 u	7.5 u

Total number of biscuits that Pamela and Sarah have
= 7 u + 8 u
= 15 u 

Number of biscuits that Pamela and Sarah each has in the end is the same.

Number of biscuits that Pamela and Sarah each has in the end in Case 2
= 15 u ÷ 2
= 7.5 u

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

7.5 u + 8 = 7 u + 36
7.5 u - 7 u = 36 - 8
0.5 u = 28

1 u = 28 ÷ 0.5 = 56

Number of biscuits that Sarah has
= 8 u - 36
= 8 x 56 - 36
= 448 - 36
= 412

Answer(s): 412