Vanessa and Xylia have some cupcakes each. If Vanessa gives Xylia 19 cupcakes, Vanessa will have ⁵₈ as many cupcakes as Xylia. If Vanessa gives Xylia 11 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Vanessa have at first?

	Case 1		Case 2
	Vanessa	Xylia	Vanessa	Xylia
Before	5 u + 19	8 u - 19	6.5 u + 11	6.5 u - 11
Change	- 19	+ 19	- 11	+ 11
After	5 u	8 u	6.5 u	6.5 u

Total number of cupcakes that Vanessa and Xylia have
= 5 u + 8 u
= 13 u 

Number of cupcakes that Vanessa and Xylia each has in the end is the same.

Number of cupcakes that Vanessa and Xylia each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u

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

6.5 u + 11 = 5 u + 19
6.5 u - 5 u = 19 - 11
0.5 u = 8

1 u = 8 ÷ 0.5 = 16

Number of cupcakes that Vanessa has
= 5 u + 19
= 5 x 16 + 19
= 80 + 19
= 99

Answer(s): 99