Barbara and Roshel have some muffins each. If Barbara gives Roshel 31 muffins, Barbara will have ²₃ as many muffins as Roshel. If Barbara gives Roshel 3 muffins, they will have an equal number of muffins. How many muffins does Roshel have at first?

	Case 1		Case 2
	Barbara	Roshel	Barbara	Roshel
Before	2 u + 31	3 u - 31	2.5 u + 3	2.5 u - 3
Change	- 31	+ 31	- 3	+ 3
After	2 u	3 u	2.5 u	2.5 u

Total number of muffins that Barbara and Roshel have
= 2 u + 3 u
= 5 u 

Number of muffins that Barbara and Roshel each has in the end is the same.

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

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

2.5 u + 3 = 2 u + 31
2.5 u - 2 u = 31 - 3
0.5 u = 28

1 u = 28 ÷ 0.5 = 56

Number of muffins that Roshel has
= 3 u - 31
= 3 x 56 - 31
= 168 - 31
= 137

Answer(s): 137