Usha and Vanessa have some cupcakes each. If Usha gives Vanessa 24 cupcakes, Usha will have ⁴₅ as many cupcakes as Vanessa. If Usha gives Vanessa 2 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Vanessa have at first?

	Case 1		Case 2
	Usha	Vanessa	Usha	Vanessa
Before	4 u + 24	5 u - 24	4.5 u + 2	4.5 u - 2
Change	- 24	+ 24	- 2	+ 2
After	4 u	5 u	4.5 u	4.5 u

Total number of cupcakes that Usha and Vanessa have
= 4 u + 5 u
= 9 u 

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

Number of cupcakes that Usha and Vanessa each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

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

4.5 u + 2 = 4 u + 24
4.5 u - 4 u = 24 - 2
0.5 u = 22

1 u = 22 ÷ 0.5 = 44

Number of cupcakes that Vanessa has
= 5 u - 24
= 5 x 44 - 24
= 220 - 24
= 196

Answer(s): 196