Sarah and Yoko have some cupcakes each. If Sarah gives Yoko 12 cupcakes, Sarah will have ⁴₉ as many cupcakes as Yoko. If Sarah gives Yoko 9 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Sarah have at first?

	Case 1		Case 2
	Sarah	Yoko	Sarah	Yoko
Before	4 u + 12	9 u - 12	6.5 u + 9	6.5 u - 9
Change	- 12	+ 12	- 9	+ 9
After	4 u	9 u	6.5 u	6.5 u

Total number of cupcakes that Sarah and Yoko have
= 4 u + 9 u
= 13 u 

Number of cupcakes that Sarah and Yoko each has in the end is the same.

Number of cupcakes that Sarah and Yoko each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u

Number of cupcakes that Sarah had at first is the same in Case 1 and Case 2.

6.5 u + 9 = 4 u + 12
6.5 u - 4 u = 12 - 9
0.5 u = 3

1 u = 3 ÷ 0.5 = 6

Number of cupcakes that Sarah has
= 4 u + 12
= 4 x 6 + 12
= 24 + 12
= 36

Answer(s): 36