Xuan and Emma have some cupcakes each. If Xuan gives Emma 7 cupcakes, Xuan will have ³₄ as many cupcakes as Emma. If Xuan gives Emma 5 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Xuan have at first?

	Case 1		Case 2
	Xuan	Emma	Xuan	Emma
Before	3 u + 7	4 u - 7	3.5 u + 5	3.5 u - 5
Change	- 7	+ 7	- 5	+ 5
After	3 u	4 u	3.5 u	3.5 u

Total number of cupcakes that Xuan and Emma have
= 3 u + 4 u
= 7 u 

Number of cupcakes that Xuan and Emma each has in the end is the same.

Number of cupcakes that Xuan and Emma each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u

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

3.5 u + 5 = 3 u + 7
3.5 u - 3 u = 7 - 5
0.5 u = 2

1 u = 2 ÷ 0.5 = 4

Number of cupcakes that Xuan has
= 3 u + 7
= 3 x 4 + 7
= 12 + 7
= 19

Answer(s): 19