Tina and Olivia have some cookies each. If Tina gives Olivia 23 cookies, Tina will have ⁴₉ as many cookies as Olivia. If Tina gives Olivia 20 cookies, they will have an equal number of cookies. How many cookies does Tina have at first?

	Case 1		Case 2
	Tina	Olivia	Tina	Olivia
Before	4 u + 23	9 u - 23	6.5 u + 20	6.5 u - 20
Change	- 23	+ 23	- 20	+ 20
After	4 u	9 u	6.5 u	6.5 u

Total number of cookies that Tina and Olivia have
= 4 u + 9 u
= 13 u 

Number of cookies that Tina and Olivia each has in the end is the same.

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

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

6.5 u + 20 = 4 u + 23
6.5 u - 4 u = 23 - 20
0.5 u = 3

1 u = 3 ÷ 0.5 = 6

Number of cookies that Tina has
= 4 u + 23
= 4 x 6 + 23
= 24 + 23
= 47

Answer(s): 47