Nora and Emma have some macarons each. If Nora gives Emma 29 macarons, Nora will have ²₅ as many macarons as Emma. If Nora gives Emma 3 macarons, they will have an equal number of macarons. How many macarons does Emma have at first?

	Case 1		Case 2
	Nora	Emma	Nora	Emma
Before	2 u + 29	5 u - 29	3.5 u + 3	3.5 u - 3
Change	- 29	+ 29	- 3	+ 3
After	2 u	5 u	3.5 u	3.5 u

Total number of macarons that Nora and Emma have
= 2 u + 5 u
= 7 u 

Number of macarons that Nora and Emma each has in the end is the same.

Number of macarons that Nora and Emma each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u

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

3.5 u + 3 = 2 u + 29
3.5 u - 2 u = 29 - 3
0.5 u = 26

1 u = 26 ÷ 0.5 = 52

Number of macarons that Emma has
= 5 u - 29
= 5 x 52 - 29
= 260 - 29
= 231

Answer(s): 231