Jen and Nora have some cupcakes each. If Jen gives Nora 33 cupcakes, Jen will have ⁵₈ as many cupcakes as Nora. If Jen gives Nora 9 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Nora have at first?

	Case 1		Case 2
	Jen	Nora	Jen	Nora
Before	5 u + 33	8 u - 33	6.5 u + 9	6.5 u - 9
Change	- 33	+ 33	- 9	+ 9
After	5 u	8 u	6.5 u	6.5 u

Total number of cupcakes that Jen and Nora have
= 5 u + 8 u
= 13 u 

Number of cupcakes that Jen and Nora each has in the end is the same.

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

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

6.5 u + 9 = 5 u + 33
6.5 u - 5 u = 33 - 9
0.5 u = 24

1 u = 24 ÷ 0.5 = 48

Number of cupcakes that Nora has
= 8 u - 33
= 8 x 48 - 33
= 384 - 33
= 351

Answer(s): 351