Zoe and Raeann have some biscuits each. If Zoe gives Raeann 12 biscuits, Zoe will have ⁷₈ as many biscuits as Raeann. If Zoe gives Raeann 4 biscuits, they will have an equal number of biscuits. How many biscuits does Zoe have at first?

	Case 1		Case 2
	Zoe	Raeann	Zoe	Raeann
Before	7 u + 12	8 u - 12	7.5 u + 4	7.5 u - 4
Change	- 12	+ 12	- 4	+ 4
After	7 u	8 u	7.5 u	7.5 u

Total number of biscuits that Zoe and Raeann have
= 7 u + 8 u
= 15 u 

Number of biscuits that Zoe and Raeann each has in the end is the same.

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

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

7.5 u + 4 = 7 u + 12
7.5 u - 7 u = 12 - 4
0.5 u = 8

1 u = 8 ÷ 0.5 = 16

Number of biscuits that Zoe has
= 7 u + 12
= 7 x 16 + 12
= 112 + 12
= 124

Answer(s): 124