Roshel and Jane have some cupcakes each. If Roshel gives Jane 22 cupcakes, Roshel will have ⁵₈ as many cupcakes as Jane. If Roshel gives Jane 14 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Roshel have at first?

	Case 1		Case 2
	Roshel	Jane	Roshel	Jane
Before	5 u + 22	8 u - 22	6.5 u + 14	6.5 u - 14
Change	- 22	+ 22	- 14	+ 14
After	5 u	8 u	6.5 u	6.5 u

Total number of cupcakes that Roshel and Jane have
= 5 u + 8 u
= 13 u 

Number of cupcakes that Roshel and Jane each has in the end is the same.

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

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

6.5 u + 14 = 5 u + 22
6.5 u - 5 u = 22 - 14
0.5 u = 8

1 u = 8 ÷ 0.5 = 16

Number of cupcakes that Roshel has
= 5 u + 22
= 5 x 16 + 22
= 80 + 22
= 102

Answer(s): 102