Gillian and Kathy have some cookies each. If Gillian gives Kathy 21 cookies, Gillian will have ⁴₉ as many cookies as Kathy. If Gillian gives Kathy 18 cookies, they will have an equal number of cookies. How many cookies does Gillian have at first?

	Case 1		Case 2
	Gillian	Kathy	Gillian	Kathy
Before	4 u + 21	9 u - 21	6.5 u + 18	6.5 u - 18
Change	- 21	+ 21	- 18	+ 18
After	4 u	9 u	6.5 u	6.5 u

Total number of cookies that Gillian and Kathy have
= 4 u + 9 u
= 13 u 

Number of cookies that Gillian and Kathy each has in the end is the same.

Number of cookies that Gillian and Kathy each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u

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

6.5 u + 18 = 4 u + 21
6.5 u - 4 u = 21 - 18
0.5 u = 3

1 u = 3 ÷ 0.5 = 6

Number of cookies that Gillian has
= 4 u + 21
= 4 x 6 + 21
= 24 + 21
= 45

Answer(s): 45