Elyse and Yoko have some cupcakes each. If Elyse gives Yoko 24 cupcakes, Elyse will have ⁵₈ as many cupcakes as Yoko. If Elyse gives Yoko 19 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Elyse have at first?

	Case 1		Case 2
	Elyse	Yoko	Elyse	Yoko
Before	5 u + 24	8 u - 24	6.5 u + 19	6.5 u - 19
Change	- 24	+ 24	- 19	+ 19
After	5 u	8 u	6.5 u	6.5 u

Total number of cupcakes that Elyse and Yoko have
= 5 u + 8 u
= 13 u 

Number of cupcakes that Elyse and Yoko each has in the end is the same.

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

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

6.5 u + 19 = 5 u + 24
6.5 u - 5 u = 24 - 19
0.5 u = 5

1 u = 5 ÷ 0.5 = 10

Number of cupcakes that Elyse has
= 5 u + 24
= 5 x 10 + 24
= 50 + 24
= 74

Answer(s): 74