Jane and Jade had a total of 98 buttons. Jade gave ¹₄ of her buttons to Jane. In return, Jane gave ¹₈ of the total number of buttons that she had to Jade. In the end, each girl had the same number of buttons. How many buttons did Jane have at first?

	Jane	Jade	Total
Before 1	?	4 u	98
Change 1	+ 1 u	- 1 u
After 1	56	3 u	98
Before 2	8 p	3 u	98
Change 2	- 1 p	+ 1 p
After 2	7 p (49)	49	98

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

Number of buttons that Jade and Jane each had in the end is the same.

Number of buttons that Jane had in the end
= 98 ÷ 2
= 49

Number of buttons that Jane had in the end = 7 p

7 p = 49

1 p = 49 ÷ 7 = 7

Number of buttons that Jane had after receiving some buttons from Jade
= 8 p
= 8 x 7
= 56

Number of buttons that Jade had after giving to Jane
= 98 - 56
= 42

3 u = 42

1 u = 42 ÷ 3 = 14

Number of buttons that Jade had at first
= 4 u
= 4 x 14
= 56

Number of buttons that Jane had at first
= 98 - 56
= 42

Answer(s): 42