Shannon and Erika have some muffins each. If Shannon gives Erika 15 muffins, Shannon will have ²₃ as many muffins as Erika. If Shannon gives Erika 6 muffins, they will have an equal number of muffins. How many muffins does Shannon have at first?

	Case 1		Case 2
	Shannon	Erika	Shannon	Erika
Before	2 u + 15	3 u - 15	2.5 u + 6	2.5 u - 6
Change	- 15	+ 15	- 6	+ 6
After	2 u	3 u	2.5 u	2.5 u

Total number of muffins that Shannon and Erika have
= 2 u + 3 u
= 5 u 

Number of muffins that Shannon and Erika each has in the end is the same.

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

Number of muffins that Shannon had at first is the same in Case 1 and Case 2.

2.5 u + 6 = 2 u + 15
2.5 u - 2 u = 15 - 6
0.5 u = 9

1 u = 9 ÷ 0.5 = 18

Number of muffins that Shannon has
= 2 u + 15
= 2 x 18 + 15
= 36 + 15
= 51

Answer(s): 51