Opal and Gwen have some cookies each. If Opal gives Gwen 29 cookies, Opal will have ¹₂ as many cookies as Gwen. If Opal gives Gwen 19 cookies, they will have an equal number of cookies. How many cookies does Opal have at first?

	Case 1		Case 2
	Opal	Gwen	Opal	Gwen
Before	1 u + 29	2 u - 29	1.5 u + 19	1.5 u - 19
Change	- 29	+ 29	- 19	+ 19
After	1 u	2 u	1.5 u	1.5 u

Total number of cookies that Opal and Gwen have
= 1 u + 2 u
= 3 u 

Number of cookies that Opal and Gwen each has in the end is the same.

Number of cookies that Opal and Gwen each has in the end in Case 2
= 3 u ÷ 2
= 1.5 u

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

1.5 u + 19 = 1 u + 29
1.5 u - 1 u = 29 - 19
0.5 u = 10

1 u = 10 ÷ 0.5 = 20

Number of cookies that Opal has
= 1 u + 29
= 1 x 20 + 29
= 20 + 29
= 49

Answer(s): 49