Erika and Emily have some cupcakes each. If Erika gives Emily 23 cupcakes, Erika will have ¹₄ as many cupcakes as Emily. If Erika gives Emily 10 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Emily have at first?

	Case 1		Case 2
	Erika	Emily	Erika	Emily
Before	1 u + 23	4 u - 23	2.5 u + 10	2.5 u - 10
Change	- 23	+ 23	- 10	+ 10
After	1 u	4 u	2.5 u	2.5 u

Total number of cupcakes that Erika and Emily have
= 1 u + 4 u
= 5 u 

Number of cupcakes that Erika and Emily each has in the end is the same.

Number of cupcakes that Erika and Emily each has in the end in Case 2
= 5 u ÷ 2
= 2.5 u

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

2.5 u + 10 = 1 u + 23
2.5 u - 1 u = 23 - 10
0.5 u = 13

1 u = 13 ÷ 0.5 = 26

Number of cupcakes that Emily has
= 4 u - 23
= 4 x 26 - 23
= 104 - 23
= 81

Answer(s): 81