Esther and Jane have some cupcakes each. If Esther gives Jane 26 cupcakes, Esther will have ⁴₉ as many cupcakes as Jane. If Esther gives Jane 19 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Esther have at first?

	Case 1		Case 2
	Esther	Jane	Esther	Jane
Before	4 u + 26	9 u - 26	6.5 u + 19	6.5 u - 19
Change	- 26	+ 26	- 19	+ 19
After	4 u	9 u	6.5 u	6.5 u

Total number of cupcakes that Esther and Jane have
= 4 u + 9 u
= 13 u 

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

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

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

6.5 u + 19 = 4 u + 26
6.5 u - 4 u = 26 - 19
0.5 u = 7

1 u = 7 ÷ 0.5 = 14

Number of cupcakes that Esther has
= 4 u + 26
= 4 x 14 + 26
= 56 + 26
= 82

Answer(s): 82