Gillian and Xandra have some cupcakes each. If Gillian gives Xandra 26 cupcakes, Gillian will have ⁵₆ as many cupcakes as Xandra. If Gillian gives Xandra 2 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Xandra have at first?

	Case 1		Case 2
	Gillian	Xandra	Gillian	Xandra
Before	5 u + 26	6 u - 26	5.5 u + 2	5.5 u - 2
Change	- 26	+ 26	- 2	+ 2
After	5 u	6 u	5.5 u	5.5 u

Total number of cupcakes that Gillian and Xandra have
= 5 u + 6 u
= 11 u 

Number of cupcakes that Gillian and Xandra each has in the end is the same.

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

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

5.5 u + 2 = 5 u + 26
5.5 u - 5 u = 26 - 2
0.5 u = 24

1 u = 24 ÷ 0.5 = 48

Number of cupcakes that Xandra has
= 6 u - 26
= 6 x 48 - 26
= 288 - 26
= 262

Answer(s): 262