Nora and Lynn have some cupcakes each. If Nora gives Lynn 19 cupcakes, Nora will have ²₇ as many cupcakes as Lynn. If Nora gives Lynn 6 cupcakes, they will have an equal number of cupcakes. How many cupcakes does Lynn have at first?

	Case 1		Case 2
	Nora	Lynn	Nora	Lynn
Before	2 u + 19	7 u - 19	4.5 u + 6	4.5 u - 6
Change	- 19	+ 19	- 6	+ 6
After	2 u	7 u	4.5 u	4.5 u

Total number of cupcakes that Nora and Lynn have
= 2 u + 7 u
= 9 u 

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

Number of cupcakes that Nora and Lynn each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

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

4.5 u + 6 = 2 u + 19
4.5 u - 2 u = 19 - 6
0.5 u = 13

1 u = 13 ÷ 0.5 = 26

Number of cupcakes that Lynn has
= 7 u - 19
= 7 x 26 - 19
= 182 - 19
= 163

Answer(s): 163