Penelope and Risa have some cookies each. If Penelope gives Risa 27 cookies, Penelope will have ⁸₉ as many cookies as Risa. If Penelope gives Risa 18 cookies, they will have an equal number of cookies. How many cookies does Penelope have at first?

	Case 1		Case 2
	Penelope	Risa	Penelope	Risa
Before	8 u + 27	9 u - 27	8.5 u + 18	8.5 u - 18
Change	- 27	+ 27	- 18	+ 18
After	8 u	9 u	8.5 u	8.5 u

Total number of cookies that Penelope and Risa have
= 8 u + 9 u
= 17 u 

Number of cookies that Penelope and Risa each has in the end is the same.

Number of cookies that Penelope and Risa each has in the end in Case 2
= 17 u ÷ 2
= 8.5 u

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

8.5 u + 18 = 8 u + 27
8.5 u - 8 u = 27 - 18
0.5 u = 9

1 u = 9 ÷ 0.5 = 18

Number of cookies that Penelope has
= 8 u + 27
= 8 x 18 + 27
= 144 + 27
= 171

Answer(s): 171