Jane and Ivory have some cupcakes each. If Jane gives Ivory 25 cupcakes, Jane will have ¹₂ as many cupcakes as Ivory. If Jane gives Ivory 8 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Ivory have at first?

	Case 1		Case 2
	Jane	Ivory	Jane	Ivory
Before	1 u + 25	2 u - 25	1.5 u + 8	1.5 u - 8
Change	- 25	+ 25	- 8	+ 8
After	1 u	2 u	1.5 u	1.5 u

Total number of cupcakes that Jane and Ivory have
= 1 u + 2 u
= 3 u 

Number of cupcakes that Jane and Ivory each has in the end is the same.

Number of cupcakes that Jane and Ivory each has in the end in Case 2
= 3 u ÷ 2
= 1.5 u

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

1.5 u + 8 = 1 u + 25
1.5 u - 1 u = 25 - 8
0.5 u = 17

1 u = 17 ÷ 0.5 = 34

Number of cupcakes that Ivory has
= 2 u - 25
= 2 x 34 - 25
= 68 - 25
= 43

Answer(s): 43