Olivia and Jaslyn had a total of 108 buttons. Jaslyn gave ¹₄ of her buttons to Olivia. In return, Olivia gave ¹₇ of the total number of buttons that she had to Jaslyn. In the end, each girl had the same number of buttons. How many buttons did Olivia have at first?

	Olivia	Jaslyn	Total
Before 1	?	4 u	108
Change 1	+ 1 u	- 1 u
After 1	63	3 u	108
Before 2	7 p	3 u	108
Change 2	- 1 p	+ 1 p
After 2	6 p (54)	54	108

Since Jaslyn gave some buttons to Olivia and Olivia then gave some buttons to Jaslyn, it is an internal transfer of buttons between the two girls. So, the total number of buttons remains unchanged.

Number of buttons that Jaslyn and Olivia each had in the end is the same.

Number of buttons that Olivia had in the end
= 108 ÷ 2
= 54

Number of buttons that Olivia had in the end = 6 p

6 p = 54

1 p = 54 ÷ 6 = 9

Number of buttons that Olivia had after receiving some buttons from Jaslyn
= 7 p
= 7 x 9
= 63

Number of buttons that Jaslyn had after giving to Olivia
= 108 - 63
= 45

3 u = 45

1 u = 45 ÷ 3 = 15

Number of buttons that Jaslyn had at first
= 4 u
= 4 x 15
= 60

Number of buttons that Olivia had at first
= 108 - 60
= 48

Answer(s): 48