Dana and Olivia have some muffins each. If Dana gives Olivia 13 muffins, Dana will have ¹₂ as many muffins as Olivia. If Dana gives Olivia 10 muffins, they will have an equal number of muffins. How many muffins does Dana have at first?

	Case 1		Case 2
	Dana	Olivia	Dana	Olivia
Before	1 u + 13	2 u - 13	1.5 u + 10	1.5 u - 10
Change	- 13	+ 13	- 10	+ 10
After	1 u	2 u	1.5 u	1.5 u

Total number of muffins that Dana and Olivia have
= 1 u + 2 u
= 3 u 

Number of muffins that Dana and Olivia each has in the end is the same.

Number of muffins that Dana and Olivia each has in the end in Case 2
= 3 u ÷ 2
= 1.5 u

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

1.5 u + 10 = 1 u + 13
1.5 u - 1 u = 13 - 10
0.5 u = 3

1 u = 3 ÷ 0.5 = 6

Number of muffins that Dana has
= 1 u + 13
= 1 x 6 + 13
= 6 + 13
= 19

Answer(s): 19