Jean and Erika have some cupcakes each. If Jean gives Erika 30 cupcakes, Jean will have ⁵₈ as many cupcakes as Erika. If Jean gives Erika 2 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Erika have at first?

	Case 1		Case 2
	Jean	Erika	Jean	Erika
Before	5 u + 30	8 u - 30	6.5 u + 2	6.5 u - 2
Change	- 30	+ 30	- 2	+ 2
After	5 u	8 u	6.5 u	6.5 u

Total number of cupcakes that Jean and Erika have
= 5 u + 8 u
= 13 u 

Number of cupcakes that Jean and Erika each has in the end is the same.

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

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

6.5 u + 2 = 5 u + 30
6.5 u - 5 u = 30 - 2
0.5 u = 28

1 u = 28 ÷ 0.5 = 56

Number of cupcakes that Erika has
= 8 u - 30
= 8 x 56 - 30
= 448 - 30
= 418

Answer(s): 418