Sarah and Irene have some muffins each. If Sarah gives Irene 19 muffins, Sarah will have ³₄ as many muffins as Irene. If Sarah gives Irene 16 muffins, they will have an equal number of muffins. How many muffins does Sarah have at first?

	Case 1		Case 2
	Sarah	Irene	Sarah	Irene
Before	3 u + 19	4 u - 19	3.5 u + 16	3.5 u - 16
Change	- 19	+ 19	- 16	+ 16
After	3 u	4 u	3.5 u	3.5 u

Total number of muffins that Sarah and Irene have
= 3 u + 4 u
= 7 u 

Number of muffins that Sarah and Irene each has in the end is the same.

Number of muffins that Sarah and Irene each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u

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

3.5 u + 16 = 3 u + 19
3.5 u - 3 u = 19 - 16
0.5 u = 3

1 u = 3 ÷ 0.5 = 6

Number of muffins that Sarah has
= 3 u + 19
= 3 x 6 + 19
= 18 + 19
= 37

Answer(s): 37