Yen and Rachel have some cookies each. If Yen gives Rachel 27 cookies, Yen will have ²₇ as many cookies as Rachel. If Yen gives Rachel 4 cookies, they will have an equal number of cookies. How many cookies does Rachel have at first?

	Case 1		Case 2
	Yen	Rachel	Yen	Rachel
Before	2 u + 27	7 u - 27	4.5 u + 4	4.5 u - 4
Change	- 27	+ 27	- 4	+ 4
After	2 u	7 u	4.5 u	4.5 u

Total number of cookies that Yen and Rachel have
= 2 u + 7 u
= 9 u 

Number of cookies that Yen and Rachel each has in the end is the same.

Number of cookies that Yen and Rachel each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

Number of cookies that Yen had at first is the same in Case 1 and Case 2.

4.5 u + 4 = 2 u + 27
4.5 u - 2 u = 27 - 4
0.5 u = 23

1 u = 23 ÷ 0.5 = 46

Number of cookies that Rachel has
= 7 u - 27
= 7 x 46 - 27
= 322 - 27
= 295

Answer(s): 295