Jean and Fred collect coins and buttons. Fred has 96 more buttons than coins. Fred has 3 times the number of coins Jean has, and Jean has 25% more buttons than Fred. After Jean gives Fred all of her coins and Fred gives Jean 75% of his buttons, Fred has 28 more coins than buttons. Find the number of buttons Jean has at first.

Jean		Fred
Buttons	Coins	Buttons	Coins
3.75 u + 120	1 u	3 u + 96	3 u
+ 2.25 u + 72	- 1 u	- 2.25 u - 72	+ 1 u
6 u + 192	0	0.75 u + 24	4 u

100% + 25% = 125% 

125% x 3 u
= ¹²⁵₁₀₀ x 3 u
= 3.75 u

125% x 96
= ¹²⁵₁₀₀ x 96
= 120 

75% x 3 u
= ⁷⁵₁₀₀ x 3 u
= 2.25 u  

75% x 96 
= ⁷⁵₁₀₀ x 96
= 72 

If another 28 buttons are given to Fred, he will have equal number of buttons and coins in the end.
4 u = 0.75 u + 24 + 28
4 u - 0.75 u = 52
3.25 u = 52

1 u = 52 ÷ 3.25 = 16

Number of buttons that Jean has at first
= 3.75 u + 120
= 3.75 x 16 + 120
= 60 + 120
= 180
 
Answer(s): 180