Raeann and Tina have some cupcakes each. If Raeann gives Tina 38 cupcakes, Raeann will have ⁵₆ as many cupcakes as Tina. If Raeann gives Tina 10 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Tina have at first?

	Case 1		Case 2
	Raeann	Tina	Raeann	Tina
Before	5 u + 38	6 u - 38	5.5 u + 10	5.5 u - 10
Change	- 38	+ 38	- 10	+ 10
After	5 u	6 u	5.5 u	5.5 u

Total number of cupcakes that Raeann and Tina have
= 5 u + 6 u
= 11 u 

Number of cupcakes that Raeann and Tina each has in the end is the same.

Number of cupcakes that Raeann and Tina each has in the end in Case 2
= 11 u ÷ 2
= 5.5 u

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

5.5 u + 10 = 5 u + 38
5.5 u - 5 u = 38 - 10
0.5 u = 28

1 u = 28 ÷ 0.5 = 56

Number of cupcakes that Tina has
= 6 u - 38
= 6 x 56 - 38
= 336 - 38
= 298

Answer(s): 298